fft.cpp

/*
  In the name of ALLAH
  Author : Raashid Anwar
*/

#include <bits/stdc++.h>
using namespace std;

#define int int64_t
const int M1 =  998244353;
const int M2 =  1000000007;
mt19937 rng((uint64_t)chrono::steady_clock::now().time_since_epoch().count());

// https://cp-algorithms.com/algebra/fft.html

using cd = complex <double>;
const double PI = acos(-1);

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

  for (int i = 1, j = 0; i < n; i++) {
    int bit = n >> 1;
    for (; j & bit; bit >>= 1)
      j ^= bit;
    j ^= bit;

    if (i < j)
      swap(a[i], a[j]);
  }

  for (int len = 2; len <= n; len <<= 1) {
    double ang = 2.0 * PI / len * (invert ? -1.0 : 1.0);
    cd wlen(cos(ang), sin(ang));
    for (int i = 0; i < n; i += len) {
      cd w(1);
      for (int j = 0; j < len / 2; j++) {
        cd u = a[i + j], v = a[i + j + len / 2] * w;
        a[i + j] = u + v;
        a[i + j + len / 2] = u - v;
        w *= wlen;
      }
    }
  }

  if (invert) {
    for (cd & x : a)
      x /= n;
  }
}


void solve() {
  
}

int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  solve();
}