From 7eeed974efb5af1843f3292134bf03329aeb57e0 Mon Sep 17 00:00:00 2001
From: maspypy <maspypy.gmail.com>
Date: Fri, 15 Sep 2023 22:10:24 +0900
Subject: [PATCH 01/12] add problem

---
 math/gcd_of_gaussian_integers/checker.cpp     | 30 ++++++++
 math/gcd_of_gaussian_integers/gaussian.hpp    | 69 +++++++++++++++++++
 .../gen/example_00.in                         |  9 +++
 .../gen/fibonacci_like.cpp                    | 30 ++++++++
 .../gen/large_gcd.cpp                         | 38 ++++++++++
 math/gcd_of_gaussian_integers/gen/random.cpp  | 24 +++++++
 math/gcd_of_gaussian_integers/gen/small.cpp   | 32 +++++++++
 math/gcd_of_gaussian_integers/hash.json       | 26 +++++++
 math/gcd_of_gaussian_integers/info.toml       | 32 +++++++++
 math/gcd_of_gaussian_integers/sol/correct.cpp | 29 ++++++++
 .../sol/random_correct.cpp                    | 32 +++++++++
 math/gcd_of_gaussian_integers/task.md         | 61 ++++++++++++++++
 math/gcd_of_gaussian_integers/verifier.cpp    | 24 +++++++
 13 files changed, 436 insertions(+)
 create mode 100644 math/gcd_of_gaussian_integers/checker.cpp
 create mode 100644 math/gcd_of_gaussian_integers/gaussian.hpp
 create mode 100644 math/gcd_of_gaussian_integers/gen/example_00.in
 create mode 100644 math/gcd_of_gaussian_integers/gen/fibonacci_like.cpp
 create mode 100644 math/gcd_of_gaussian_integers/gen/large_gcd.cpp
 create mode 100644 math/gcd_of_gaussian_integers/gen/random.cpp
 create mode 100644 math/gcd_of_gaussian_integers/gen/small.cpp
 create mode 100644 math/gcd_of_gaussian_integers/hash.json
 create mode 100644 math/gcd_of_gaussian_integers/info.toml
 create mode 100644 math/gcd_of_gaussian_integers/sol/correct.cpp
 create mode 100644 math/gcd_of_gaussian_integers/sol/random_correct.cpp
 create mode 100644 math/gcd_of_gaussian_integers/task.md
 create mode 100644 math/gcd_of_gaussian_integers/verifier.cpp

diff --git a/math/gcd_of_gaussian_integers/checker.cpp b/math/gcd_of_gaussian_integers/checker.cpp
new file mode 100644
index 000000000..c2af14ddc
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/checker.cpp
@@ -0,0 +1,30 @@
+#include <vector>
+#include <utility>
+#include <stdint.h>
+#include <inttypes.h>
+#include "testlib.h"
+
+using namespace std;
+
+int main(int argc, char* argv[]) {
+  setName("compare sequences of tokens");
+  registerTestlibCmd(argc, argv);
+
+  int T = inf.readInt();
+
+  for (int t = 0; t < T; ++t) {
+    int ouf_a = ouf.readInt();
+    int ouf_b = ouf.readInt();
+    int ans_a = ans.readInt();
+    int ans_b = ans.readInt();
+    bool ok = 0;
+    for (int i = 0; i < 4; ++i) {
+      tie(ans_a, ans_b) = make_pair(ans_b, -ans_a);
+      if (ouf_a == ans_a && ouf_b == ans_b) ok = 1;
+    }
+    if (!ok) { quitf(_wa, "wa, gcd is not correct"); }
+  }
+  quitf(_ok, "OK");
+
+  return 0;
+}
diff --git a/math/gcd_of_gaussian_integers/gaussian.hpp b/math/gcd_of_gaussian_integers/gaussian.hpp
new file mode 100644
index 000000000..b8889981f
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/gaussian.hpp
@@ -0,0 +1,69 @@
+#include <tuple>
+
+template <typename T, typename U>
+T floor(T x, U y) {
+  return (x > 0 ? x / y : (x - y + 1) / y);
+}
+
+template <typename T>
+struct Gaussian_Integer {
+  T x, y;
+  using G = Gaussian_Integer;
+
+  Gaussian_Integer(T x = 0, T y = 0) : x(x), y(y) {}
+  Gaussian_Integer(pair<T, T> p) : x(p.fi), y(p.se) {}
+
+  T norm() const { return x * x + y * y; }
+  G conjugate() const { return G(x, -y); }
+
+  G &operator+=(const G &g) {
+    x += g.x, y += g.y;
+    return *this;
+  }
+  G &operator-=(const G &g) {
+    x -= g.x, y -= g.y;
+    return *this;
+  }
+  G &operator*=(const G &g) {
+    tie(x, y) = make_pair(x * g.x - y * g.y, x * g.y + y * g.x);
+    return *this;
+  }
+  G &operator/=(const G &g) {
+    *this *= g.conjugate();
+    T n = g.norm();
+    x = floor(x + n / 2, n);
+    y = floor(y + n / 2, n);
+    return *this;
+  }
+  G &operator%=(const G &g) {
+    auto q = G(*this) / g;
+    q *= g;
+    (*this) -= q;
+    return *this;
+  }
+  G operator-() { return G(-x, -y); }
+  G operator+(const G &g) { return G(*this) += g; }
+  G operator-(const G &g) { return G(*this) -= g; }
+  G operator*(const G &g) { return G(*this) *= g; }
+  G operator/(const G &g) { return G(*this) /= g; }
+  G operator%(const G &g) { return G(*this) %= g; }
+  bool operator==(const G &g) { return (x == g.x && y == g.y); }
+
+  static G gcd(G a, G b) {
+    while (b.x != 0 || b.y != 0) {
+      a %= b;
+      swap(a, b);
+    }
+    return a;
+  }
+
+  // (g,x,y) s.t ax+by=g
+  static tuple<G, G, G> extgcd(G a, G b) {
+    if (b.x != 0 || b.y != 0) {
+      G q = a / b;
+      auto [g, x, y] = extgcd(b, a - q * b);
+      return {g, y, x - q * y};
+    }
+    return {a, G{1, 0}, G{0, 0}};
+  }
+};
diff --git a/math/gcd_of_gaussian_integers/gen/example_00.in b/math/gcd_of_gaussian_integers/gen/example_00.in
new file mode 100644
index 000000000..6a9d41460
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/gen/example_00.in
@@ -0,0 +1,9 @@
+8
+8 0 6 0
+0 0 0 0
+0 0 4 8
+4 0 6 2
+1 2 3 4
+1 -2 3 4
+1 -3 5 -7
+-344235 225420 -33882 162741
diff --git a/math/gcd_of_gaussian_integers/gen/fibonacci_like.cpp b/math/gcd_of_gaussian_integers/gen/fibonacci_like.cpp
new file mode 100644
index 000000000..38aa602cd
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/gen/fibonacci_like.cpp
@@ -0,0 +1,30 @@
+#include <iostream>
+#include <vector>
+#include <tuple>
+
+#include "../params.h"
+#include "random.h"
+
+using namespace std;
+using ll = long long;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int T = T_MAX;
+  printf("%d\n", T);
+  for (int t = 0; t < T; ++t) {
+    ll a = 1, b = 0, c = 0, d = 0;
+    while (1) {
+      int k = gen.uniform<int>(0, 3);
+      for (int i = 0; i < k; ++i) { tie(a, b) = make_pair(b, -a); }
+      ll aa = c + a, bb = d + b, cc = a, dd = b;
+      if (min<ll>({aa, bb, cc, dd}) < MIN) break;
+      if (max<ll>({aa, bb, cc, dd}) > MAX) break;
+      a = aa, b = bb, c = cc, d = dd;
+    }
+    printf("%lld %lld %lld %lld\n", a, b, c, d);
+  }
+  return 0;
+}
diff --git a/math/gcd_of_gaussian_integers/gen/large_gcd.cpp b/math/gcd_of_gaussian_integers/gen/large_gcd.cpp
new file mode 100644
index 000000000..0c859b1a0
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/gen/large_gcd.cpp
@@ -0,0 +1,38 @@
+#include <iostream>
+#include <vector>
+#include <tuple>
+
+#include "../params.h"
+#include "random.h"
+
+using namespace std;
+using ll = long long;
+
+#include "../gaussian.hpp"
+
+using G = Gaussian_Integer<ll>;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  ll LIM1 = 1000;
+  ll LIM2 = 1000000 / 2;
+
+  auto gen_gauss = [&](ll LIM) -> G {
+    ll x = gen.uniform<int>(-LIM, LIM);
+    ll y = gen.uniform<int>(-LIM, LIM);
+    return G{x, y};
+  };
+
+  int T = T_MAX;
+  printf("%d\n", T);
+  for (int t = 0; t < T; ++t) {
+    G g = gen_gauss(LIM2);
+    G a = gen_gauss(LIM1);
+    G b = gen_gauss(LIM1);
+    a *= g, b *= g;
+    printf("%lld %lld %lld %lld\n", a.x, a.y, b.x, b.y);
+  }
+  return 0;
+}
diff --git a/math/gcd_of_gaussian_integers/gen/random.cpp b/math/gcd_of_gaussian_integers/gen/random.cpp
new file mode 100644
index 000000000..1fa85730d
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/gen/random.cpp
@@ -0,0 +1,24 @@
+#include <iostream>
+#include <vector>
+#include <tuple>
+
+#include "../params.h"
+#include "random.h"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int T = T_MAX;
+  printf("%d\n", T);
+  for (int t = 0; t < T; ++t) {
+    int a = gen.uniform<int>(MIN, MAX);
+    int b = gen.uniform<int>(MIN, MAX);
+    int c = gen.uniform<int>(MIN, MAX);
+    int d = gen.uniform<int>(MIN, MAX);
+    printf("%d %d %d %d\n", a, b, c, d);
+  }
+  return 0;
+}
diff --git a/math/gcd_of_gaussian_integers/gen/small.cpp b/math/gcd_of_gaussian_integers/gen/small.cpp
new file mode 100644
index 000000000..ba86c53b9
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/gen/small.cpp
@@ -0,0 +1,32 @@
+#include <iostream>
+#include <vector>
+#include <tuple>
+
+#include "../params.h"
+#include "random.h"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  // auto gen = Random(seed); つかわない
+
+  const int LIM = 10;
+  vector<tuple<int, int, int, int>> problems;
+  for (int a = -LIM; a <= LIM; ++a) {
+    for (int b = -LIM; b <= LIM; ++b) {
+      for (int c = -LIM; c <= LIM; ++c) {
+        for (int d = -LIM; d <= LIM; ++d) {
+          if ((a + b + c + d + seed) % 2 == 0)
+            problems.emplace_back(a, b, c, d);
+        }
+      }
+    }
+  }
+
+  int t = problems.size();
+  assert(1 <= t && t <= T_MAX);
+  printf("%d\n", t);
+  for (auto& [a, b, c, d]: problems) { printf("%d %d %d %d\n", a, b, c, d); }
+  return 0;
+}
diff --git a/math/gcd_of_gaussian_integers/hash.json b/math/gcd_of_gaussian_integers/hash.json
new file mode 100644
index 000000000..ac861dcd7
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/hash.json
@@ -0,0 +1,26 @@
+{
+  "example_00.in": "7dc4086ba8bec80ef0442494f94ecc4a3c75c95a254541287dc5cf510505e798",
+  "example_00.out": "92d60e96fca7f75cecea6765a1f5c6ef19ad8dbdcf8bd143bc68e532d136dde3",
+  "fibonacci_like_00.in": "ef21064f421a0b2a0315a720191616108a9e0ae88c6497f9dd731236ace1c772",
+  "fibonacci_like_00.out": "902c656dda476a0a456e7dd4caf007959b880058822049d404db3d8c6ab5d154",
+  "fibonacci_like_01.in": "c59c734522884d8cf794590b4ed3e3242d0cb6a0eaab2ad5ef106fc0a9d46cf2",
+  "fibonacci_like_01.out": "628b2d4bf31bd31c1ef8c7742d82d3605f2e28986ed2760e7f5c5e1277f8245b",
+  "large_gcd_00.in": "d9478f45c4f0190fc3cd3542eb6b1532511435940b5f145568479ab489a98085",
+  "large_gcd_00.out": "98db471072ba552e365fd63092889aa3db929b72071eabd6a903e5149ad657f7",
+  "large_gcd_01.in": "14ac6874495297c0018908bdedf7091f99e86321959d7e3bc31930e2b36d9fb8",
+  "large_gcd_01.out": "2d6dcdbfe2b7ed410e86d8d5bf3938db4dc85bda29ac9f9b2587233b71093b59",
+  "random_00.in": "6e05b9b9b6b78ab540355def3a15b5b66e46d4eac200f862b76b978e5ca13120",
+  "random_00.out": "e20fac6eb4c1896334f2b27b4872e3d4ae54160eda5f43b4820d0b0b5d657ccb",
+  "random_01.in": "dfc10c33c94add6e5634143aecd6e6bf9af5e75980d8d4241a46f2ca005e3415",
+  "random_01.out": "0d529841ac84c6f6ccebd368f51e31153ebdbe7c5508220f47d309e94744a5ac",
+  "random_02.in": "a041c3e17d097ebe215e9fd21e92904780812384aafd862f358251b656aa021b",
+  "random_02.out": "8435c8d791ac6ac2c119d794acecbb744b0fcb96dd6d230f5af352d3fd083099",
+  "random_03.in": "28eb47c73ecd35f46a5f9fb4b93d225fba69e0f17950eb13db5c6f716abcf0d1",
+  "random_03.out": "e0f22148a4831745357cded508e63b54883166e52ae5dc73c39fe30a9e5890ad",
+  "random_04.in": "b6077663099db878634f78b06e4ac5e113057e4e2ed4b8292bc6c2f868952f86",
+  "random_04.out": "902772158b1abb1aaee812016737848b4f932eb9b5a98f99c534f21f343e5444",
+  "small_00.in": "3cbe5b6a235266af934850e3d27399a6e9ee4785dbe017f9a8be49bb72d4a52d",
+  "small_00.out": "62f870f657880fbffa49257dc28ff258fa553744cc6fed47a05ad3463d7af4da",
+  "small_01.in": "fa819ca05c040e2e8861bb418dfdfa2af2846b5d6d548daf57e03a7a7723b66b",
+  "small_01.out": "4b1063c4c397b40d8a6733bfd2a232ea128b54605059285c7bc34733711e5b5e"
+}
\ No newline at end of file
diff --git a/math/gcd_of_gaussian_integers/info.toml b/math/gcd_of_gaussian_integers/info.toml
new file mode 100644
index 000000000..9fc53bf1c
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/info.toml
@@ -0,0 +1,32 @@
+title = 'Gcd Convolution'
+timelimit = 5.0
+forum = "https://github.com/yosupo06/library-checker-problems/issues/749"
+
+[[tests]]
+    name = "example.in"
+    number = 1
+
+[[tests]]
+    name = "small.cpp"
+    number = 2
+
+[[tests]]
+    name = "random.cpp"
+    number = 5
+
+[[tests]]
+    name = "fibonacci_like.cpp"
+    number = 2
+
+[[tests]]
+    name = "large_gcd.cpp"
+    number = 2
+
+[[solutions]]
+    name = "random_correct.cpp"
+    wrong = false
+    
+[params]
+    T_MAX = 100000
+    MIN = -1000000000
+    MAX = 1000000000
diff --git a/math/gcd_of_gaussian_integers/sol/correct.cpp b/math/gcd_of_gaussian_integers/sol/correct.cpp
new file mode 100644
index 000000000..d5e94dd32
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/sol/correct.cpp
@@ -0,0 +1,29 @@
+#include <cstdio>
+#include <vector>
+#include <cassert>
+
+using namespace std;
+using ll = long long;
+
+#include "../gaussian.hpp"
+
+using G = Gaussian_Integer<ll>;
+
+int main() {
+  int T;
+  scanf("%d", &T);
+
+  for (int t = 0; t < T; ++t) {
+    ll a1, b1, a2, b2;
+    scanf("%lld %lld %lld %lld", &a1, &b1, &a2, &b2);
+    G a(a1, b1);
+    G b(a2, b2);
+    auto [g, x, y] = G::extgcd(a, b);
+    assert(a * x + b * y == g);
+    assert((g == G{0, 0} && a == G{0, 0}) || (a % g == 0));
+    assert((g == G{0, 0} && b == G{0, 0}) || (b % g == 0));
+    printf("%lld %lld\n", g.x, g.y);
+  }
+
+  return 0;
+}
diff --git a/math/gcd_of_gaussian_integers/sol/random_correct.cpp b/math/gcd_of_gaussian_integers/sol/random_correct.cpp
new file mode 100644
index 000000000..52ef67be0
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/sol/random_correct.cpp
@@ -0,0 +1,32 @@
+#include <cstdio>
+#include <vector>
+#include <cassert>
+
+using namespace std;
+using ll = long long;
+
+#include "../gaussian.hpp"
+
+using G = Gaussian_Integer<ll>;
+
+int main() {
+  int T;
+  scanf("%d", &T);
+
+  G I{0, 1};
+
+  for (int t = 0; t < T; ++t) {
+    ll a1, b1, a2, b2;
+    scanf("%lld %lld %lld %lld", &a1, &b1, &a2, &b2);
+    G a(a1, b1);
+    G b(a2, b2);
+    auto [g, x, y] = G::extgcd(a, b);
+    assert(a * x + b * y == g);
+    assert((g == G{0, 0} && a == G{0, 0}) || (a % g == 0));
+    assert((g == G{0, 0} && b == G{0, 0}) || (b % g == 0));
+    for (int i = 0; i < t % 4; ++i) { g *= I; }
+    printf("%lld %lld\n", g.x, g.y);
+  }
+
+  return 0;
+}
diff --git a/math/gcd_of_gaussian_integers/task.md b/math/gcd_of_gaussian_integers/task.md
new file mode 100644
index 000000000..5a630b708
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/task.md
@@ -0,0 +1,61 @@
+## @{keyword.statement}
+
+@{lang.en}
+In this problem, $i$ represents the imaginary unit.
+
+Given Gaussian integers $a_1+b_1i$ and $a_2+b_2i, find one of their greatest common divisors.
+
+Please refer to the following definitions for Gaussian integers and their greatest common divisors:
+
+- An element of $\mathbb{Z}[i] = \{a+bi\mid a,b\in \mathbb{Z}}$ is called a Gaussian integer.
+
+- For $x, y \in \mathbb{Z}[i]$, we define $x\mid y$ if there exists a $z$ in $\mathbb{Z}[i]$ such that $y = xz$.
+
+- A Gaussian integer $g$ is a greatest common divisor of $x$ and $y$ in $\mathbb{Z}[i]$ if, for any $z$ in $\mathbb{Z}[i]$, the condition $g\mid z$ is equivalent to $x\mid z$ and $y\mid z$. Such a $g$ is uniquely determined except for multiples of $\pm 1$ and $\pm i$.
+
+You have $T$ test cases to solve.
+
+@{lang.ja}
+この問題において，$i$ は虚数単位を表します．
+
+Gauss 整数 $a_1+b_1i, a_2+b_2i$ が与えられるので，その最大公約数（のひとつ）を求めてください．
+
+Gauss 整数やその最大公約数については以下の定義を参考にしてください．
+
+- $\mathbb{Z}[i] = \{a+bi\mid a,b\in \mathbb{Z}}$ の元を Gauss 整数という．
+- $x,y \in \mathbb{Z}[i]$ に対し，$y=xz$ となる $z \in \mathbb{Z}[i]$ が存在するとき $x\mid y$ であると定義する．
+- $g \in \mathbb{Z}[i]$ が $x,y \mathbb{Z}[i]$ の最大公約数であるとは，任意の $z\in \mathbb{Z}[i]$ に対して $g\mid z \iff x\mid z \text{かつ} y\mid z$ が成り立つことをいう．このような $g$ は，$\pm 1$, $\pm i$ 倍の不定性を除き一意に定まる．
+
+$T$ 個のテストケースが与えられるので，それぞれについて答えを求めてください．
+
+@{lang.end}
+
+## @{keyword.constraints}
+- $1 \leq T \leq @{param.T_MAX}$
+- $@{param.MIN} \leq a_1, b_1, a_2, b_2 \leq @{param.MAX}$
+
+## @{keyword.input}
+
+```
+$N$
+$a_1$ $b_1$ $a_2$ $b_2$
+$\vdots$
+$a_1$ $b_1$ $a_2$ $b_2$
+```
+
+## @{keyword.output}
+
+When $a+bi$ is a greatest common divisor of $a_1+b_1i$ and $a_2+b_2i$, output $a$ and $b$. 
+```
+$a$ $b$
+```
+
+## @{keyword.sample}
+
+@{example.example_00}
+
+@{lang.ja}
+$1$ つめのテストケースについて，`2 0` の他に，`-2 0`, `0 2`, `0 -2` も正答となります．
+@{lang.en}
+For the first test case, in addition to `2 0`, the following answers are also correct: `-2 0`, `0 2`, and `0 -2`.
+@{lang.end}
diff --git a/math/gcd_of_gaussian_integers/verifier.cpp b/math/gcd_of_gaussian_integers/verifier.cpp
new file mode 100644
index 000000000..a0fb16459
--- /dev/null
+++ b/math/gcd_of_gaussian_integers/verifier.cpp
@@ -0,0 +1,24 @@
+#include <iostream>
+
+#include "params.h"
+#include "testlib.h"
+
+int main() {
+  registerValidation();
+  int T = inf.readInt(1, T_MAX);
+  inf.readChar('\n');
+
+  for (int t = 0; t < T; ++t) {
+    inf.readInt(MIN, MAX);
+    inf.readSpace();
+    inf.readInt(MIN, MAX);
+    inf.readSpace();
+    inf.readInt(MIN, MAX);
+    inf.readSpace();
+    inf.readInt(MIN, MAX);
+    inf.readChar('\n');
+  }
+
+  inf.readEof();
+  return 0;
+}

From 3fbfcf2dfd02dce43c190dfbced446a39ae844ce Mon Sep 17 00:00:00 2001
From: maspypy <maspypy.gmail.com>
Date: Fri, 15 Sep 2023 22:14:16 +0900
Subject: [PATCH 02/12] fix title

---
 math/gcd_of_gaussian_integers/info.toml | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/math/gcd_of_gaussian_integers/info.toml b/math/gcd_of_gaussian_integers/info.toml
index 9fc53bf1c..c38a060a8 100644
--- a/math/gcd_of_gaussian_integers/info.toml
+++ b/math/gcd_of_gaussian_integers/info.toml
@@ -1,6 +1,6 @@
-title = 'Gcd Convolution'
+title = 'Gcd of Gaussian Integers'
 timelimit = 5.0
-forum = "https://github.com/yosupo06/library-checker-problems/issues/749"
+forum = "https://github.com/yosupo06/library-checker-problems/issues/958"
 
 [[tests]]
     name = "example.in"

From 18facdbf1e476aab4874e6623d7f29dc310b77d8 Mon Sep 17 00:00:00 2001
From: maspypy <maspypy.gmail.com>
Date: Fri, 15 Sep 2023 22:17:40 +0900
Subject: [PATCH 03/12] fix

---
 math/gcd_of_gaussian_integers/checker.cpp | 1 -
 math/gcd_of_gaussian_integers/task.md     | 2 +-
 2 files changed, 1 insertion(+), 2 deletions(-)

diff --git a/math/gcd_of_gaussian_integers/checker.cpp b/math/gcd_of_gaussian_integers/checker.cpp
index c2af14ddc..9c29b5ec5 100644
--- a/math/gcd_of_gaussian_integers/checker.cpp
+++ b/math/gcd_of_gaussian_integers/checker.cpp
@@ -25,6 +25,5 @@ int main(int argc, char* argv[]) {
     if (!ok) { quitf(_wa, "wa, gcd is not correct"); }
   }
   quitf(_ok, "OK");
-
   return 0;
 }
diff --git a/math/gcd_of_gaussian_integers/task.md b/math/gcd_of_gaussian_integers/task.md
index 5a630b708..6af8b44a5 100644
--- a/math/gcd_of_gaussian_integers/task.md
+++ b/math/gcd_of_gaussian_integers/task.md
@@ -3,7 +3,7 @@
 @{lang.en}
 In this problem, $i$ represents the imaginary unit.
 
-Given Gaussian integers $a_1+b_1i$ and $a_2+b_2i, find one of their greatest common divisors.
+Given Gaussian integers $a_1+b_1i$ and $a_2+b_2i$, find one of their greatest common divisors.
 
 Please refer to the following definitions for Gaussian integers and their greatest common divisors:
 

From 9a431d8dcddfe2d1d8630ce426516237c94205ca Mon Sep 17 00:00:00 2001
From: maspypy <maspypy.gmail.com>
Date: Fri, 15 Sep 2023 22:21:07 +0900
Subject: [PATCH 04/12] fix

---
 math/gcd_of_gaussian_integers/task.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/math/gcd_of_gaussian_integers/task.md b/math/gcd_of_gaussian_integers/task.md
index 6af8b44a5..beb2d04dc 100644
--- a/math/gcd_of_gaussian_integers/task.md
+++ b/math/gcd_of_gaussian_integers/task.md
@@ -7,7 +7,7 @@ Given Gaussian integers $a_1+b_1i$ and $a_2+b_2i$, find one of their greatest co
 
 Please refer to the following definitions for Gaussian integers and their greatest common divisors:
 
-- An element of $\mathbb{Z}[i] = \{a+bi\mid a,b\in \mathbb{Z}}$ is called a Gaussian integer.
+- An element of $\mathbb{Z}[i] = \lbrace a+bi\mid a,b\in \mathbb{Z}\rbrace$ is called a Gaussian integer.
 
 - For $x, y \in \mathbb{Z}[i]$, we define $x\mid y$ if there exists a $z$ in $\mathbb{Z}[i]$ such that $y = xz$.
 
@@ -22,7 +22,7 @@ Gauss 整数 $a_1+b_1i, a_2+b_2i$ が与えられるので，その最大公約
 
 Gauss 整数やその最大公約数については以下の定義を参考にしてください．
 
-- $\mathbb{Z}[i] = \{a+bi\mid a,b\in \mathbb{Z}}$ の元を Gauss 整数という．
+- $\mathbb{Z}[i] = \lbrace a+bi\mid a,b\in \mathbb{Z} \rbrace$ の元を Gauss 整数という．
 - $x,y \in \mathbb{Z}[i]$ に対し，$y=xz$ となる $z \in \mathbb{Z}[i]$ が存在するとき $x\mid y$ であると定義する．
 - $g \in \mathbb{Z}[i]$ が $x,y \mathbb{Z}[i]$ の最大公約数であるとは，任意の $z\in \mathbb{Z}[i]$ に対して $g\mid z \iff x\mid z \text{かつ} y\mid z$ が成り立つことをいう．このような $g$ は，$\pm 1$, $\pm i$ 倍の不定性を除き一意に定まる．
 

From c72029e999b660f549e4b96c43e97f075855b9c2 Mon Sep 17 00:00:00 2001
From: maspypy <maspypy.gmail.com>
Date: Fri, 15 Sep 2023 22:22:23 +0900
Subject: [PATCH 05/12] a

---
 math/gcd_of_gaussian_integers/task.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/math/gcd_of_gaussian_integers/task.md b/math/gcd_of_gaussian_integers/task.md
index beb2d04dc..5254628f5 100644
--- a/math/gcd_of_gaussian_integers/task.md
+++ b/math/gcd_of_gaussian_integers/task.md
@@ -11,7 +11,7 @@ Please refer to the following definitions for Gaussian integers and their greate
 
 - For $x, y \in \mathbb{Z}[i]$, we define $x\mid y$ if there exists a $z$ in $\mathbb{Z}[i]$ such that $y = xz$.
 
-- A Gaussian integer $g$ is a greatest common divisor of $x$ and $y$ in $\mathbb{Z}[i]$ if, for any $z$ in $\mathbb{Z}[i]$, the condition $g\mid z$ is equivalent to $x\mid z$ and $y\mid z$. Such a $g$ is uniquely determined except for multiples of $\pm 1$ and $\pm i$.
+- A Gaussian integer $g$ is a greatest common divisor of $x, y\in \mathbb{Z}[i]$ if, for any $z$ in $\mathbb{Z}[i]$, the condition $g\mid z$ is equivalent to $x\mid z$ and $y\mid z$. Such a $g$ is uniquely determined except for multiples of $\pm 1$ and $\pm i$.
 
 You have $T$ test cases to solve.
 
@@ -24,7 +24,7 @@ Gauss 整数やその最大公約数については以下の定義を参考に
 
 - $\mathbb{Z}[i] = \lbrace a+bi\mid a,b\in \mathbb{Z} \rbrace$ の元を Gauss 整数という．
 - $x,y \in \mathbb{Z}[i]$ に対し，$y=xz$ となる $z \in \mathbb{Z}[i]$ が存在するとき $x\mid y$ であると定義する．
-- $g \in \mathbb{Z}[i]$ が $x,y \mathbb{Z}[i]$ の最大公約数であるとは，任意の $z\in \mathbb{Z}[i]$ に対して $g\mid z \iff x\mid z \text{かつ} y\mid z$ が成り立つことをいう．このような $g$ は，$\pm 1$, $\pm i$ 倍の不定性を除き一意に定まる．
+- $g \in \mathbb{Z}[i]$ が $x,y \in \mathbb{Z}[i]$ の最大公約数であるとは，任意の $z\in \mathbb{Z}[i]$ に対して $g\mid z \iff x\mid z \text{かつ} y\mid z$ が成り立つことをいう．このような $g$ は，$\pm 1$, $\pm i$ 倍の不定性を除き一意に定まる．
 
 $T$ 個のテストケースが与えられるので，それぞれについて答えを求めてください．
 

From 9f128d29c90cb478fd9b4e75d1807c64da1b04f0 Mon Sep 17 00:00:00 2001
From: maspypy <maspypy.gmail.com>
Date: Fri, 15 Sep 2023 22:23:00 +0900
Subject: [PATCH 06/12] a

---
 math/gcd_of_gaussian_integers/task.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/math/gcd_of_gaussian_integers/task.md b/math/gcd_of_gaussian_integers/task.md
index 5254628f5..d4863522f 100644
--- a/math/gcd_of_gaussian_integers/task.md
+++ b/math/gcd_of_gaussian_integers/task.md
@@ -37,7 +37,7 @@ $T$ 個のテストケースが与えられるので，それぞれについて
 ## @{keyword.input}
 
 ```
-$N$
+$T$
 $a_1$ $b_1$ $a_2$ $b_2$
 $\vdots$
 $a_1$ $b_1$ $a_2$ $b_2$

From e6c0311e6f61615a4b6bb068232f3d205052be60 Mon Sep 17 00:00:00 2001
From: maspypy <maspypy.gmail.com>
Date: Fri, 15 Sep 2023 22:30:42 +0900
Subject: [PATCH 07/12] def of gcd

---
 math/gcd_of_gaussian_integers/task.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/math/gcd_of_gaussian_integers/task.md b/math/gcd_of_gaussian_integers/task.md
index d4863522f..47f828823 100644
--- a/math/gcd_of_gaussian_integers/task.md
+++ b/math/gcd_of_gaussian_integers/task.md
@@ -11,7 +11,7 @@ Please refer to the following definitions for Gaussian integers and their greate
 
 - For $x, y \in \mathbb{Z}[i]$, we define $x\mid y$ if there exists a $z$ in $\mathbb{Z}[i]$ such that $y = xz$.
 
-- A Gaussian integer $g$ is a greatest common divisor of $x, y\in \mathbb{Z}[i]$ if, for any $z$ in $\mathbb{Z}[i]$, the condition $g\mid z$ is equivalent to $x\mid z$ and $y\mid z$. Such a $g$ is uniquely determined except for multiples of $\pm 1$ and $\pm i$.
+- A Gaussian integer $g$ is a greatest common divisor of $x, y\in \mathbb{Z}[i]$ if, for any $z$ in $\mathbb{Z}[i]$, the condition $z\mid g$ is equivalent to $z\mid x$ and $z\mid y$. Such a $g$ is uniquely determined except for multiples of $\pm 1$ and $\pm i$.
 
 You have $T$ test cases to solve.
 
@@ -24,7 +24,7 @@ Gauss 整数やその最大公約数については以下の定義を参考に
 
 - $\mathbb{Z}[i] = \lbrace a+bi\mid a,b\in \mathbb{Z} \rbrace$ の元を Gauss 整数という．
 - $x,y \in \mathbb{Z}[i]$ に対し，$y=xz$ となる $z \in \mathbb{Z}[i]$ が存在するとき $x\mid y$ であると定義する．
-- $g \in \mathbb{Z}[i]$ が $x,y \in \mathbb{Z}[i]$ の最大公約数であるとは，任意の $z\in \mathbb{Z}[i]$ に対して $g\mid z \iff x\mid z \text{かつ} y\mid z$ が成り立つことをいう．このような $g$ は，$\pm 1$, $\pm i$ 倍の不定性を除き一意に定まる．
+- $g \in \mathbb{Z}[i]$ が $x,y \in \mathbb{Z}[i]$ の最大公約数であるとは，任意の $z\in \mathbb{Z}[i]$ に対して $z\mid g \iff z\mid x \text{かつ} z\mid y$ が成り立つことをいう．このような $g$ は，$\pm 1$, $\pm i$ 倍の不定性を除き一意に定まる．
 
 $T$ 個のテストケースが与えられるので，それぞれについて答えを求めてください．
 

From b161ad2f54e0e31734ce2d0d8ed11df094b73d67 Mon Sep 17 00:00:00 2001
From: maspypy <maspypy.gmail.com>
Date: Thu, 21 Sep 2023 20:47:00 +0900
Subject: [PATCH 08/12] upd task.md

---
 math/gcd_of_gaussian_integers/task.md | 10 +++++++---
 1 file changed, 7 insertions(+), 3 deletions(-)

diff --git a/math/gcd_of_gaussian_integers/task.md b/math/gcd_of_gaussian_integers/task.md
index 47f828823..3820c8970 100644
--- a/math/gcd_of_gaussian_integers/task.md
+++ b/math/gcd_of_gaussian_integers/task.md
@@ -11,7 +11,7 @@ Please refer to the following definitions for Gaussian integers and their greate
 
 - For $x, y \in \mathbb{Z}[i]$, we define $x\mid y$ if there exists a $z$ in $\mathbb{Z}[i]$ such that $y = xz$.
 
-- A Gaussian integer $g$ is a greatest common divisor of $x, y\in \mathbb{Z}[i]$ if, for any $z$ in $\mathbb{Z}[i]$, the condition $z\mid g$ is equivalent to $z\mid x$ and $z\mid y$. Such a $g$ is uniquely determined except for multiples of $\pm 1$ and $\pm i$.
+- A Gaussian integer $g$ is a greatest common divisor of $x, y\in \mathbb{Z}[i]$ if, for any $z$ in $\mathbb{Z}[i]$, $z\mid g \iff z\mid x\wedge z \mid y$ holds. Such a $g$ is uniquely determined except for multiples of $\pm 1$ and $\pm i$.
 
 You have $T$ test cases to solve.
 
@@ -24,7 +24,7 @@ Gauss 整数やその最大公約数については以下の定義を参考に
 
 - $\mathbb{Z}[i] = \lbrace a+bi\mid a,b\in \mathbb{Z} \rbrace$ の元を Gauss 整数という．
 - $x,y \in \mathbb{Z}[i]$ に対し，$y=xz$ となる $z \in \mathbb{Z}[i]$ が存在するとき $x\mid y$ であると定義する．
-- $g \in \mathbb{Z}[i]$ が $x,y \in \mathbb{Z}[i]$ の最大公約数であるとは，任意の $z\in \mathbb{Z}[i]$ に対して $z\mid g \iff z\mid x \text{かつ} z\mid y$ が成り立つことをいう．このような $g$ は，$\pm 1$, $\pm i$ 倍の不定性を除き一意に定まる．
+- $g \in \mathbb{Z}[i]$ が $x,y \in \mathbb{Z}[i]$ の最大公約数であるとは，任意の $z\in \mathbb{Z}[i]$ に対して，$z\mid g \iff z\mid x\wedge z \mid y$ が成り立つことをいう．このような $g$ は，$\pm 1$, $\pm i$ 倍の不定性を除き一意に定まる．
 
 $T$ 個のテストケースが与えられるので，それぞれについて答えを求めてください．
 
@@ -44,8 +44,12 @@ $a_1$ $b_1$ $a_2$ $b_2$
 ```
 
 ## @{keyword.output}
-
+@{lang.ja}
+$a_1+b_1i$ と $a_2+b_2i$ の最大公約数が $a+bi$ であるとき，$a, b$ を出力してください．
+@{lang.en}
 When $a+bi$ is a greatest common divisor of $a_1+b_1i$ and $a_2+b_2i$, output $a$ and $b$. 
+@{lang.end}
+
 ```
 $a$ $b$
 ```

From daad4e1c8d8b1d0bd5bad41e1fc34358b515b9b2 Mon Sep 17 00:00:00 2001
From: maspypy <maspypy.gmail.com>
Date: Thu, 21 Sep 2023 20:56:45 +0900
Subject: [PATCH 09/12] upd task

---
 math/gcd_of_gaussian_integers/task.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/math/gcd_of_gaussian_integers/task.md b/math/gcd_of_gaussian_integers/task.md
index 3820c8970..fa7640369 100644
--- a/math/gcd_of_gaussian_integers/task.md
+++ b/math/gcd_of_gaussian_integers/task.md
@@ -11,7 +11,7 @@ Please refer to the following definitions for Gaussian integers and their greate
 
 - For $x, y \in \mathbb{Z}[i]$, we define $x\mid y$ if there exists a $z$ in $\mathbb{Z}[i]$ such that $y = xz$.
 
-- A Gaussian integer $g$ is a greatest common divisor of $x, y\in \mathbb{Z}[i]$ if, for any $z$ in $\mathbb{Z}[i]$, $z\mid g \iff z\mid x\wedge z \mid y$ holds. Such a $g$ is uniquely determined except for multiples of $\pm 1$ and $\pm i$.
+- A Gaussian integer $g$ is a greatest common divisor of $x, y\in \mathbb{Z}[i]$ if, for any $z$ in $\mathbb{Z}[i]$, the condition $z\mid g$ is equivalent to $z\mid x$ and $z\mid y$. Such a $g$ is uniquely determined except for multiples of $\pm 1$ and $\pm i$.
 
 You have $T$ test cases to solve.
 
@@ -24,7 +24,7 @@ Gauss 整数やその最大公約数については以下の定義を参考に
 
 - $\mathbb{Z}[i] = \lbrace a+bi\mid a,b\in \mathbb{Z} \rbrace$ の元を Gauss 整数という．
 - $x,y \in \mathbb{Z}[i]$ に対し，$y=xz$ となる $z \in \mathbb{Z}[i]$ が存在するとき $x\mid y$ であると定義する．
-- $g \in \mathbb{Z}[i]$ が $x,y \in \mathbb{Z}[i]$ の最大公約数であるとは，任意の $z\in \mathbb{Z}[i]$ に対して，$z\mid g \iff z\mid x\wedge z \mid y$ が成り立つことをいう．このような $g$ は，$\pm 1$, $\pm i$ 倍の不定性を除き一意に定まる．
+- $g \in \mathbb{Z}[i]$ が $x,y \in \mathbb{Z}[i]$ の最大公約数であるとは，任意の $z\in \mathbb{Z}[i]$ に対して，$z\mid g$ であることとと $z\mid x$ かつ $z\mid y$ であることが同値になることをいう．このような $g$ は，$\pm 1$, $\pm i$ 倍の不定性を除き一意に定まる．
 
 $T$ 個のテストケースが与えられるので，それぞれについて答えを求めてください．
 

From d93e4bb46e71d94b8cd5a8feda42913acf759ec6 Mon Sep 17 00:00:00 2001
From: maspypy <maspypy.gmail.com>
Date: Thu, 21 Sep 2023 21:00:59 +0900
Subject: [PATCH 10/12] typo

---
 math/gcd_of_gaussian_integers/task.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/math/gcd_of_gaussian_integers/task.md b/math/gcd_of_gaussian_integers/task.md
index fa7640369..4277f7828 100644
--- a/math/gcd_of_gaussian_integers/task.md
+++ b/math/gcd_of_gaussian_integers/task.md
@@ -24,7 +24,7 @@ Gauss 整数やその最大公約数については以下の定義を参考に
 
 - $\mathbb{Z}[i] = \lbrace a+bi\mid a,b\in \mathbb{Z} \rbrace$ の元を Gauss 整数という．
 - $x,y \in \mathbb{Z}[i]$ に対し，$y=xz$ となる $z \in \mathbb{Z}[i]$ が存在するとき $x\mid y$ であると定義する．
-- $g \in \mathbb{Z}[i]$ が $x,y \in \mathbb{Z}[i]$ の最大公約数であるとは，任意の $z\in \mathbb{Z}[i]$ に対して，$z\mid g$ であることとと $z\mid x$ かつ $z\mid y$ であることが同値になることをいう．このような $g$ は，$\pm 1$, $\pm i$ 倍の不定性を除き一意に定まる．
+- $g \in \mathbb{Z}[i]$ が $x,y \in \mathbb{Z}[i]$ の最大公約数であるとは，任意の $z\in \mathbb{Z}[i]$ に対して，$z\mid g$ であることと $z\mid x$ かつ $z\mid y$ であることが同値になることをいう．このような $g$ は，$\pm 1$, $\pm i$ 倍の不定性を除き一意に定まる．
 
 $T$ 個のテストケースが与えられるので，それぞれについて答えを求めてください．
 

From 248a4e0576f94b36526d8b1bfd20b0e6edb0f29e Mon Sep 17 00:00:00 2001
From: maspypy <maspypy.gmail.com>
Date: Wed, 25 Oct 2023 23:01:34 +0900
Subject: [PATCH 11/12] fix typo

---
 math/min_plus_convolution_convex_arbitrary/task.md | 2 +-
 math/min_plus_convolution_convex_convex/task.md    | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/math/min_plus_convolution_convex_arbitrary/task.md b/math/min_plus_convolution_convex_arbitrary/task.md
index ec56cbd33..98b1b9aa5 100644
--- a/math/min_plus_convolution_convex_arbitrary/task.md
+++ b/math/min_plus_convolution_convex_arbitrary/task.md
@@ -8,7 +8,7 @@ $$c_k = \min_{i+j=k} (a_i+b_j)$$
 @{lang.ja}
 整数列 $a_0, a_1, ..., a_{N - 1}$、$b_0, b_1, ..., b_{M - 1}$ が与えられます。ここで $a$ は凸です。次のように定義される整数列 $c_0, c_1, ..., c_{(N - 1) + (M - 1)}$ を求めてください。
 
-$$c_k = \min_{i+j=k} a_ib_j$$
+$$c_k = \min_{i+j=k} (a_i+b_j)$$
 
 @{lang.end}
 
diff --git a/math/min_plus_convolution_convex_convex/task.md b/math/min_plus_convolution_convex_convex/task.md
index 543d658da..4ebd0f5d5 100644
--- a/math/min_plus_convolution_convex_convex/task.md
+++ b/math/min_plus_convolution_convex_convex/task.md
@@ -8,7 +8,7 @@ $$c_k = \min_{i+j=k} (a_i+b_j)$$
 @{lang.ja}
 整数列 $a_0, a_1, ..., a_{N - 1}$、$b_0, b_1, ..., b_{M - 1}$ が与えられます。ここで $a$ と $b$ は凸です。次のように定義される整数列 $c_0, c_1, ..., c_{(N - 1) + (M - 1)}$ を求めてください。
 
-$$c_k = \min_{i+j=k} a_ib_j$$
+$$c_k = \min_{i+j=k} (a_i+b_j)$$
 
 @{lang.end}
 

From e14c65102a01833227058da8e55539fee72b5850 Mon Sep 17 00:00:00 2001
From: maspypy <maspypy.gmail.com>
Date: Wed, 25 Oct 2023 23:18:55 +0900
Subject: [PATCH 12/12] add testcase

---
 math/tetration_mod/gen/small_ab.cpp | 22 ++++++++++++++++++++++
 math/tetration_mod/hash.json        |  8 +++++---
 math/tetration_mod/info.toml        |  3 +++
 3 files changed, 30 insertions(+), 3 deletions(-)
 create mode 100644 math/tetration_mod/gen/small_ab.cpp

diff --git a/math/tetration_mod/gen/small_ab.cpp b/math/tetration_mod/gen/small_ab.cpp
new file mode 100644
index 000000000..a8cf8cfd9
--- /dev/null
+++ b/math/tetration_mod/gen/small_ab.cpp
@@ -0,0 +1,22 @@
+#include "random.h"
+#include <iostream>
+
+using namespace std;
+using ll = long long;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+  int l = 10;
+  int t = l * l * l;
+  printf("%d\n", t);
+  for (int a = 0; a < l; a++) {
+    for (int b = 0; b < l; b++) {
+      for (int m = 1; m <= l; m++) {
+        int mod = gen.uniform(1LL, 1'000'000'000LL);
+        printf("%d %d %d\n", a, b, mod);
+      }
+    }
+  }
+  return 0;
+}
diff --git a/math/tetration_mod/hash.json b/math/tetration_mod/hash.json
index c50859fbe..6d4c214e3 100644
--- a/math/tetration_mod/hash.json
+++ b/math/tetration_mod/hash.json
@@ -1,10 +1,10 @@
 {
+  "2_3_32_00.in": "2201a5eac58b1f044d18bd8e93ac52c296695554d4dc438a71a302ae60a6c31d",
+  "2_3_32_00.out": "e6c21e8d260fe71882debdb339d2402a2ca7648529bc2303f48649bce0380017",
   "example_00.in": "a656c75f3fc4674755fda4c12c7a541e78c2bb6cd877a5820c5966396fdccf73",
   "example_00.out": "80277aeae69bba3640d89312d1584c3a6b7c9a1bec1ebbccdf6d56cb52d2277e",
   "example_01.in": "a328ed46e2dceb7f04184d61b71f96ebd19a63a6b73835b2a29e9eb8785fd2b0",
   "example_01.out": "868ccaf4564d4d45e456fa19f3e9403a5eeeab9c9682d1caa427b34a96214533",
-  "2_3_32_00.in": "2201a5eac58b1f044d18bd8e93ac52c296695554d4dc438a71a302ae60a6c31d",
-  "2_3_32_00.out": "e6c21e8d260fe71882debdb339d2402a2ca7648529bc2303f48649bce0380017",
   "max_00.in": "cbe52808c641625f958a98505f1723cc2e24869d9ab9e59b82d39a276e89b47b",
   "max_00.out": "e36e52f693c336439495df602af57081b7335e39d6696e4c5004fcff412dccde",
   "max_01.in": "3d6c908a88a4d8d5edbc9d88cd1997f543205d6ae3af401723fbaaf225eb2671",
@@ -34,5 +34,7 @@
   "random_04.in": "55d86c94e704f451ae30384bb76bc7699e3f4a0bb94f9e70012b31640e96827f",
   "random_04.out": "42495b3a8975e2edd34f777065353a5fa85eaa14bf67b32264c2631f86260470",
   "small_00.in": "670f3cc1d60cb8f36e85a35417b8859bcf458bf447dfa30c0bc58cd20dd433bf",
-  "small_00.out": "acc9801b0d2f0c83131b9e89bd76eb5fcaee7e193555f59bcbf565fa53eaab0a"
+  "small_00.out": "acc9801b0d2f0c83131b9e89bd76eb5fcaee7e193555f59bcbf565fa53eaab0a",
+  "small_ab_00.in": "a46e93fa20c52079fde6f64f73f6768638f57ca7f0287a5ed84310bb7d58e2a0",
+  "small_ab_00.out": "f8a94948019a087a2dce5eb5489456b816aa24016fd0b12bd078eca939e75a4c"
 }
\ No newline at end of file
diff --git a/math/tetration_mod/info.toml b/math/tetration_mod/info.toml
index ac93b0940..f2bebaf45 100644
--- a/math/tetration_mod/info.toml
+++ b/math/tetration_mod/info.toml
@@ -8,6 +8,9 @@ forum = "https://github.com/yosupo06/library-checker-problems/issues/166"
 [[tests]]
     name = "small.cpp"
     number = 1
+[[tests]]
+    name = "small_ab.cpp"
+    number = 1
 [[tests]]
     name = "2_3_32.in"
     number = 1