return [=[
void fft(vector<complex<ld>>& y, bool idft) {
    int n = y.size();
    vector<int> rev(n);
    for (int i = 0; i < n; ++i) {
        rev[i] = rev[i >> 1] >> 1;
        if (i & 1) {
            rev[i] |= n >> 1;
        }
    }
    for (int i = 0; i < n; ++i) {
        if (i < rev[i]) {
            swap(y[i], y[rev[i]]);
        }
    }
    for (int h = 2; h <= n; h <<= 1) {
        complex<ld> wn(cos(2 * M_PI / h), sin(2 * M_PI / h));
        for (int j = 0; j < n; j += h) {
            complex<ld> w(1);
            for (int k = j; k < j + h / 2; ++k) {
                complex<ld> u = y[k], t = w * y[k + h / 2];
                y[k] = u + t;
                y[k + h / 2] = u - t;
                w *= wn;
            }
        }
    }
    if (idft) {
        reverse(y.begin() + 1, y.end());
        for (int i = 0; i < n; ++i) {
            y[i] /= n;
        }
    }
}

vector<int> multiply(const vector<int>& a, const vector<int>& b) {
    vector<complex<ld>> A(a.begin(), a.end()), B(b.begin(), b.end());
    int n = 1;
    while (n < a.size() + b.size()) n <<= 1;
    A.resize(n), B.resize(n);
    fft(A, false), fft(B, false);
    for (int i = 0; i < n; ++i) {
        A[i] *= B[i];
    }
    fft(A, true);
    vector<int> res(n);
    transform(A.begin(), A.end(), res.begin(), expr(int(round(x.real())), auto&& x));
    res.resize(a.size() + b.size() - 1);
    return res;
}

]=]