text: /**
   * Author: chilli
   * Date: 2019-04-16
   * License: CC0
   * Source: based on KACTL's FFT
   * Description: ntt(a) computes $\hat f(k) = \sum_x a[x] g^{xk}$ for all $k$, where $g=\text{root}^{(mod-1)/N}$.
   * N must be a power of 2.
   * Useful for convolution modulo specific nice primes of the form $2^a b+1$,
   * where the convolution result has size at most $2^a$. For arbitrary modulo, see FFTMod.
     \texttt{conv(a, b) = c}, where $c[x] = \sum a[i]b[x-i]$.
     For manual convolution: NTT the inputs, multiply
     pointwise, divide by n, reverse(start+1, end), NTT back.
   * Inputs must be in [0, mod).
   * Time: O(N \log N)
   * Status: stress-tested
   */
  
  const ll mod = (119 << 23) + 1, root = 62; // = 998244353
  // For p < 2^30 there is also e.g. 5 << 25, 7 << 26, 479 << 21
  // and 483 << 21 (same root). The last two are > 10^9.
  typedef vector<ll> vl;
  
  ll modpow(ll b, ll e) {
  	ll ans = 1;
  	for (; e; b = b * b % mod, e /= 2)
  		if (e & 1) ans = ans * b % mod;
  	return ans;
  }
  
  void ntt(vl &a) {
  	int n = sz(a), L = 31 - __builtin_clz(n);
  	static vl rt(2, 1);
  	for (static int k = 2, s = 2; k < n; k *= 2, s++) {
  		rt.resize(n);
  		ll z[] = {1, modpow(root, mod >> s)};
  		rep(i,k,2*k) rt[i] = rt[i / 2] * z[i & 1] % mod;
  	}
  	vi rev(n);
  	rep(i,0,n) rev[i] = (rev[i / 2] | (i & 1) << L) / 2;
  	rep(i,0,n) if (i < rev[i]) swap(a[i], a[rev[i]]);
  	for (int k = 1; k < n; k *= 2)
  		for (int i = 0; i < n; i += 2 * k) rep(j,0,k) {
  			ll z = rt[j + k] * a[i + j + k] % mod, &ai = a[i + j];
  			a[i + j + k] = ai - z + (z > ai ? mod : 0);
  			ai += (ai + z >= mod ? z - mod : z);
  		}
  }
  vl conv(const vl &a, const vl &b) {
  	if (a.empty() || b.empty()) return {};
  	int s = sz(a) + sz(b) - 1, B = 32 - __builtin_clz(s), n = 1 << B;
  	int inv = modpow(n, mod - 2);
  	vl L(a), R(b), out(n);
  	L.resize(n), R.resize(n);
  	ntt(L), ntt(R);
  	rep(i,0,n) out[-i & (n - 1)] = (ll)L[i] * R[i] % mod * inv % mod;
  	ntt(out);
  	return {out.begin(), out.begin() + s};
  }
  