diff --git a/.secret_cpp/bench_psi.cpp b/.secret_cpp/bench_psi.cpp
index b67090b..6df6913 100644
--- a/.secret_cpp/bench_psi.cpp
+++ b/.secret_cpp/bench_psi.cpp
@@ -1,4 +1,3 @@
-
 #include <random>
 #include <algorithm>
 #include "qpx.hpp"
@@ -89,12 +88,9 @@ static void BinarySearchesLookup(benchmark::State& state) {
   std::sort(psi.begin(), psi.end());
 
   std::vector<det_t> vals{psi.begin(), psi.end()};
-  std::vector<bool> result(vals.size());
+  std::vector<bool> result(vals.size(), false);
 
-  for(auto _ : state) {
-    binary_searchs(psi.begin(), psi.end(), vals.begin(), vals.end(), vals.begin() + vals.size() / 2,
-                   result.begin() + vals.size() / 2);
-  }
+  for(auto _ : state) { binary_searchs(psi, vals, result); }
 
   state.counters["LookupRate"] =
       benchmark::Counter(psi.size(), benchmark::Counter::kIsIterationInvariantRate);
diff --git a/.secret_cpp/category.cpp b/.secret_cpp/category.cpp
index 1a65f0c..8fd39fd 100644
--- a/.secret_cpp/category.cpp
+++ b/.secret_cpp/category.cpp
@@ -6,7 +6,9 @@
 #include <unordered_map>
 #include <vector>
 #include <array>
+#if !defined(DOCTEST_CONFIG_DISABLE)
 #define DOCTEST_CONFIG_IMPLEMENT_WITH_MAIN
+#endif
 #include <doctest/doctest.h>
 #include <qpx.hpp>
 
diff --git a/.secret_cpp/include/psi.hpp b/.secret_cpp/include/psi.hpp
index 1aa6d22..599bfba 100644
--- a/.secret_cpp/include/psi.hpp
+++ b/.secret_cpp/include/psi.hpp
@@ -1,16 +1,17 @@
 #pragma once
 
 template<class ForwardIterator, class ForwardIteratorBool>
-void binary_searchs(ForwardIterator first, ForwardIterator last, ForwardIterator v_first,
-                    ForwardIterator v_last, ForwardIterator v, ForwardIteratorBool i) {
-  // Return:  `*v` ∈? [first, last)
-  // Precondition: `v` ∈ `v_first`, `v_last`.
+void binary_searchs_imp(ForwardIterator first, ForwardIterator last, ForwardIterator v_first,
+                        ForwardIterator v_last, ForwardIterator v, ForwardIteratorBool i) {
+  // Return:       *v ∈? [first, last).
+  // Precondition: v ∈ [v_first, v_last)
 
-  // pos of `*v` inside `v` array using binary search
+  // pos is pointer ∈ [first, last) pointing `*v`.
   auto pos = std::lower_bound(first, last, *v);
-  // Find it or not find it?
-  *i = (pos != last && !(*v < *pos));
-  // Find new values to search for
+  // Lazy: only set i, if found
+  if(pos != last && !(*v < *pos)) *i = true;
+
+  // Find the new `v` to search for
   // v_first     v                v_last
   // |-----------|----------------|
   {
@@ -18,18 +19,19 @@ void binary_searchs(ForwardIterator first, ForwardIterator last, ForwardIterator
     // End the recursion when v_first == v, we search for all our values
     // if distance == 1, need to search for v_first
     auto d = std::distance(v_first, v);
-    if(pos != first && d > 1) binary_searchs(first, pos, v_first, v - 1, v - d / 2, i - d / 2);
+    if(pos != first && d > 0)
+      binary_searchs_imp(first, pos, v_first, v - 1, v - (d + 1) / 2, i - (d + 1) / 2);
   }
   {
     // Top Half (v, v_last)
     // We cannot deference v_last, so we stop the recursion when d == 1
     auto d = std::distance(v, v_last);
-    if(pos != last && d > 1) binary_searchs(pos, last, v + 1, v_last, v + d / 2, i + d / 2);
+    if(pos != last && d > 1) binary_searchs_imp(pos, last, v + 1, v_last, v + d / 2, i + d / 2);
   }
 }
 
-template<class T1, class T2, class T3>
-void binary_searchs(T1& enumerable, T2& values, T3& result) {
-  binary_searchs(enumerable.begin(), enumerable.end(), values.begin(), values.end(),
-                 values.begin() + values.size() / 2, result.begin() + values.size() / 2);
+template<class T1, class T2>
+void binary_searchs(T1& enumerable, T1& values, T2& result) {
+  binary_searchs_imp(enumerable.begin(), enumerable.end(), values.begin(), values.end(),
+                     values.begin() + values.size() / 2, result.begin() + values.size() / 2);
 }
diff --git a/.secret_cpp/include/qpx.hpp b/.secret_cpp/include/qpx.hpp
index 534f72d..4105d0e 100644
--- a/.secret_cpp/include/qpx.hpp
+++ b/.secret_cpp/include/qpx.hpp
@@ -56,7 +56,8 @@ struct std::hash<det_t> {
   }
 };
 
-std::ostream& operator<<(std::ostream& os, const det_t& obj) {
+// Should be moved in the cpp of det
+inline std::ostream& operator<<(std::ostream& os, const det_t& obj) {
   return os << "(" << obj.alpha << "," << obj.beta << ")";
 }