fft.cpp

#define _CRT_SECURE_NO_DEPRECATE
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
#include "bits/stdc++.h"
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
//using namespace __gnu_pbds;
#define int long long int
#define SYNC std::ios_base::sync_with_stdio(0);cin.tie(NULL);cout.tie(NULL);
#define FRE freopen("input.txt","r",stdin);freopen("output.txt","w",stdout);
typedef long double ld;
typedef pair<int,int> ii;
typedef pair<int,ii> iii;
typedef vector<int> vi;
typedef vector<ii>   vii;
//typedef tree<int, null_type, less<int>, rb_tree_tag,
//             tree_order_statistics_node_update>
//    ost;
#define rep(i,l,r)   for (int i = (l); i < (r); i++)
#define here cout << " Hey!!\n";
#define  pb push_back
#define  F  first
#define  S  second
#define all(v) (v).begin(),(v).end()
#define sz(a) (int)((a).size())
#define sq(x) ((x)*(x))
template <typename T>
void etch(T V) {
    for (auto x : V)    cout << x << ' ' ;
    cout << '\n';
}
vector<string> vec_splitter(string s) {
    s += ',';
    vector<string> res;
    while(!s.empty()) {
        res.push_back(s.substr(0, s.find(',')));
        s = s.substr(s.find(',') + 1);
    }
    return res;
}
void debug_out(
        vector<string> __attribute__ ((unused)) args,
        __attribute__ ((unused)) int idx,
        __attribute__ ((unused)) int LINE_NUM) { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(vector<string> args, int idx, int LINE_NUM, Head H, Tail... T) {
    if(idx > 0) cerr << ", "; else cerr << "Line(" << LINE_NUM << ") ";
    stringstream ss; ss << H;
    cerr << args[idx] << " = " << ss.str();
    debug_out(args, idx + 1, LINE_NUM, T...);
}
#ifndef ONLINE_JUDGE
#define debug(...) debug_out(vec_splitter(#__VA_ARGS__), 0, __LINE__, __VA_ARGS__)
#else
#define debug(...) 42
#endif
const int MOD = 1e9+7;
const int MOD1 = 998244353;
const int N = 2e5+5;
const int INF = 1000111000111000111LL;
const ld EPS = 1e-12;
const ld PI = 3.141592653589793116;

using cd = complex<double>;

void fft(vector<cd> & a, bool invert) 
{
    int n = a.size();
    if (n == 1)
        return;

    vector<cd> a0(n / 2), a1(n / 2);
    for (int i = 0; 2 * i < n; i++) {
        a0[i] = a[2*i];
        a1[i] = a[2*i+1];
    }
    fft(a0, invert);
    fft(a1, invert);

    double ang = 2 * PI / n * (invert ? -1 : 1);
    cd w(1), wn(cos(ang), sin(ang));
    for (int i = 0; 2 * i < n; i++) {
        a[i] = a0[i] + w * a1[i];
        a[i + n/2] = a0[i] - w * a1[i];
        if (invert) {
            a[i] /= 2;
            a[i + n/2] /= 2;
        }
        w *= wn;
    }
}

vector<int> multiply(vector<int> const& a, vector<int> const& b) 
{
    vector<cd> fa(a.begin(), a.end()), fb(b.begin(), b.end());
    int n = 1;
    while (n < a.size() + b.size()) 
        n <<= 1;
    fa.resize(n);
    fb.resize(n);

    fft(fa, false);
    fft(fb, false);
    for (int i = 0; i < n; i++)
        fa[i] *= fb[i];
    fft(fa, true);

    vector<int> result(n);
    for (int i = 0; i < n; i++)
        result[i] = round(fa[i].real());
    return result;
}


int32_t main()
{
    SYNC
    int n, x; cin >> n >> x;
    vector<int> a(n), pre(n+1, 0), fre(n+1, 0);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        a[i] = (a[i] < x) ? 1 : 0;
    }
    for (int i = 1; i <= n; i++) {
        pre[i] = pre[i-1] + a[i-1];
    }
    for (int &x : pre)  fre[x]++;

    vector<int> rev_fre = fre, sub_sums, ans(n+1, 0);
    reverse(all(rev_fre));
    sub_sums = multiply(fre, rev_fre);
    // etch(sub_sums);
    ans[0] = (sub_sums[n] - (n + 1))/2;
    for (int i = 1; i <= n; i++) {
        ans[i] = sub_sums[n+i];
    }
    etch(ans);
    return 0;
}