#pragma once
#include "rader-ntt.hpp"
template <typename mint>
struct ArbitraryLengthNTT {
using i64 = long long;
int factor(int n) {
for (int i = 2; i * i <= n; i++)
if (n % i == 0) return i;
return n;
}
vector<int> divisor(int n) {
vector<int> ret;
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) {
ret.push_back(i);
ret.push_back(n / i);
}
}
ret.push_back(n);
sort(begin(ret), end(ret));
ret.erase(unique(begin(ret), end(ret)), end(ret));
return ret;
}
int len;
vector<mint> w;
vector<int> divisors;
map<int, RaderNTT<mint> *> rader;
ArbitraryLengthNTT(int len_ = -1) { set_len(len_); }
void set_len(int len_ = -1) {
int mod = mint::get_mod();
if ((len = len_) == -1) len = mod - 1;
if (mod >= 3 && len <= 1) len = 2;
while ((mod - 1) % len != 0) ++len;
mint pr = mint(constexpr_primitive_root(mod)).pow((mod - 1) / len);
w.resize(len + 1);
for (int i = 0; i <= len; i++) w[i] = i ? w[i - 1] * pr : mint(1);
divisors = divisor(len);
}
void dft(vector<mint> &a) {
int N = a.size();
if (N == 2) {
mint a01 = a[0] + a[1];
a[1] = a[0] - a[1];
a[0] = a01;
return;
}
int d = len / N;
vector<mint> b(N);
for (int i = 0, dk = 0; i < N; i++, dk += d) {
for (int j = 0, k = 0; j < N; j++) {
b[j] += a[i] * w[k];
if ((k += dk) >= len) k -= len;
}
}
swap(a, b);
}
void ntt_base2(vector<mint> &a) {
static vector<int> btr;
int N = a.size();
assert(N % 2 == 0);
if (btr.size() != a.size()) {
btr.resize(N);
int b = __builtin_ctz(N);
assert(N == (1 << b));
for (int i = 0; i < N; i++) {
btr[i] = (btr[i >> 1] >> 1) + ((i & 1) << (b - 1));
}
}
static vector<mint> basis;
if (basis.size() < a.size()) {
basis.resize(N);
mint b = w[len / N];
for (int i = N >> 1; i > 0; i >>= 1) {
mint c = 1;
for (int j = 0; j < i; ++j) {
basis[i + j] = c;
c *= b;
}
b *= b;
}
}
for (int i = 0; i < N; i++)
if (i < btr[i]) swap(a[i], a[btr[i]]);
for (int k = 1; k < N; k <<= 1) {
for (int i = 0; i < N; i += 2 * k) {
for (int j = 0; j < k; j++) {
mint z = a[i + j + k] * basis[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
void pntt(vector<mint> &a) {
int P = a.size();
if (P <= 64) {
dft(a);
return;
}
if (rader.find(P) == end(rader)) rader[P] = new RaderNTT<mint>(P, len, w);
rader[P]->ntt(a);
}
void ntt(vector<mint> &a) {
assert(len % a.size() == 0);
int N = (int)a.size();
if (N <= 1) return;
if (N <= 64) {
dft(a);
return;
}
int P = factor(N);
if (P == N) {
pntt(a);
return;
}
if (P == 2) {
P = 1 << __builtin_ctz(N);
if (N == P) {
ntt_base2(a);
return;
}
}
int Q = N / P;
vector<mint> t(N), u(P);
{
vector<mint> s(Q);
for (int p = 0, lN = len / N, d = 0; p < P; p++, d += lN) {
for (int q = 0, qP = 0; q < Q; q++, qP += P) s[q] = a[qP + p];
ntt(s);
for (int r = 0, n = 0, pQ = p * Q; r < Q; ++r, n += d) {
t[pQ + r] = w[n] * s[r];
}
}
}
for (int r = 0; r < Q; r++) {
for (int p = 0, pQ = 0; p < P; p++, pQ += Q) u[p] = t[pQ + r];
if (P <= 64)
dft(u);
else if (P & 1)
pntt(u);
else
ntt_base2(u);
for (int s = 0, sQ = 0; s < P; s++, sQ += Q) a[sQ + r] = u[s];
}
}
void intt(vector<mint> &a) {
reverse(begin(a) + 1, end(a));
ntt(a);
mint invn = mint(a.size()).inverse();
for (auto &x : a) x *= invn;
}
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
int N = (int)a.size() + (int)b.size() - 1;
assert(N <= len);
vector<mint> s(a), t(b);
int l = *lower_bound(begin(divisors), end(divisors), N);
s.resize(l, mint(0));
t.resize(l, mint(0));
ntt(s);
ntt(t);
for (int i = 0; i < l; i++) s[i] *= t[i];
intt(s);
s.resize(N);
return s;
}
};
/**
* @brief Cooley-Tukey FFT Algorithm
*/
#line 2 "ntt/cooley-tukey-ntt.hpp"
#line 2 "ntt/rader-ntt.hpp"
#line 2 "math/constexpr-primitive-root.hpp"
constexpr unsigned int constexpr_primitive_root(unsigned int mod) {
using u32 = unsigned int;
using u64 = unsigned long long;
if(mod == 2) return 1;
u64 m = mod - 1, ds[32] = {}, idx = 0;
for (u64 i = 2; i * i <= m; ++i) {
if (m % i == 0) {
ds[idx++] = i;
while (m % i == 0) m /= i;
}
}
if (m != 1) ds[idx++] = m;
for (u32 _pr = 2, flg = true;; _pr++, flg = true) {
for (u32 i = 0; i < idx && flg; ++i) {
u64 a = _pr, b = (mod - 1) / ds[i], r = 1;
for (; b; a = a * a % mod, b >>= 1)
if (b & 1) r = r * a % mod;
if (r == 1) flg = false;
}
if (flg == true) return _pr;
}
}
#line 2 "ntt/arbitrary-ntt.hpp"
#line 2 "modint/montgomery-modint.hpp"
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
static_assert(r * mod == 1, "this code has bugs.");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint operator+() const { return mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const {
int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, u -= t * v;
tmp = x, x = y, y = tmp;
tmp = u, u = v, v = tmp;
}
return mint{u};
}
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
#line 2 "ntt/ntt.hpp"
template <typename mint>
struct NTT {
static constexpr uint32_t get_pr() {
uint32_t _mod = mint::get_mod();
using u64 = uint64_t;
u64 ds[32] = {};
int idx = 0;
u64 m = _mod - 1;
for (u64 i = 2; i * i <= m; ++i) {
if (m % i == 0) {
ds[idx++] = i;
while (m % i == 0) m /= i;
}
}
if (m != 1) ds[idx++] = m;
uint32_t _pr = 2;
while (1) {
int flg = 1;
for (int i = 0; i < idx; ++i) {
u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
while (b) {
if (b & 1) r = r * a % _mod;
a = a * a % _mod;
b >>= 1;
}
if (r == 1) {
flg = 0;
break;
}
}
if (flg == 1) break;
++_pr;
}
return _pr;
};
static constexpr uint32_t mod = mint::get_mod();
static constexpr uint32_t pr = get_pr();
static constexpr int level = __builtin_ctzll(mod - 1);
mint dw[level], dy[level];
void setwy(int k) {
mint w[level], y[level];
w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
y[k - 1] = w[k - 1].inverse();
for (int i = k - 2; i > 0; --i)
w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
for (int i = 3; i < k; ++i) {
dw[i] = dw[i - 1] * y[i - 2] * w[i];
dy[i] = dy[i - 1] * w[i - 2] * y[i];
}
}
NTT() { setwy(level); }
void fft4(vector<mint> &a, int k) {
if ((int)a.size() <= 1) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
if (k & 1) {
int v = 1 << (k - 1);
for (int j = 0; j < v; ++j) {
mint ajv = a[j + v];
a[j + v] = a[j] - ajv;
a[j] += ajv;
}
}
int u = 1 << (2 + (k & 1));
int v = 1 << (k - 2 - (k & 1));
mint one = mint(1);
mint imag = dw[1];
while (v) {
// jh = 0
{
int j0 = 0;
int j1 = v;
int j2 = j1 + v;
int j3 = j2 + v;
for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
}
}
// jh >= 1
mint ww = one, xx = one * dw[2], wx = one;
for (int jh = 4; jh < u;) {
ww = xx * xx, wx = ww * xx;
int j0 = jh * v;
int je = j0 + v;
int j2 = je + v;
for (; j0 < je; ++j0, ++j2) {
mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
t3 = a[j2 + v] * wx;
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
}
xx *= dw[__builtin_ctzll((jh += 4))];
}
u <<= 2;
v >>= 2;
}
}
void ifft4(vector<mint> &a, int k) {
if ((int)a.size() <= 1) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
int u = 1 << (k - 2);
int v = 1;
mint one = mint(1);
mint imag = dy[1];
while (u) {
// jh = 0
{
int j0 = 0;
int j1 = v;
int j2 = v + v;
int j3 = j2 + v;
for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
}
}
// jh >= 1
mint ww = one, xx = one * dy[2], yy = one;
u <<= 2;
for (int jh = 4; jh < u;) {
ww = xx * xx, yy = xx * imag;
int j0 = jh * v;
int je = j0 + v;
int j2 = je + v;
for (; j0 < je; ++j0, ++j2) {
mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
}
xx *= dy[__builtin_ctzll(jh += 4)];
}
u >>= 4;
v <<= 2;
}
if (k & 1) {
u = 1 << (k - 1);
for (int j = 0; j < u; ++j) {
mint ajv = a[j] - a[j + u];
a[j] += a[j + u];
a[j + u] = ajv;
}
}
}
void ntt(vector<mint> &a) {
if ((int)a.size() <= 1) return;
fft4(a, __builtin_ctz(a.size()));
}
void intt(vector<mint> &a) {
if ((int)a.size() <= 1) return;
ifft4(a, __builtin_ctz(a.size()));
mint iv = mint(a.size()).inverse();
for (auto &x : a) x *= iv;
}
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
int l = a.size() + b.size() - 1;
if (min<int>(a.size(), b.size()) <= 40) {
vector<mint> s(l);
for (int i = 0; i < (int)a.size(); ++i)
for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
return s;
}
int k = 2, M = 4;
while (M < l) M <<= 1, ++k;
setwy(k);
vector<mint> s(M);
for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
fft4(s, k);
if (a.size() == b.size() && a == b) {
for (int i = 0; i < M; ++i) s[i] *= s[i];
} else {
vector<mint> t(M);
for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
fft4(t, k);
for (int i = 0; i < M; ++i) s[i] *= t[i];
}
ifft4(s, k);
s.resize(l);
mint invm = mint(M).inverse();
for (int i = 0; i < l; ++i) s[i] *= invm;
return s;
}
void ntt_doubling(vector<mint> &a) {
int M = (int)a.size();
auto b = a;
intt(b);
mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;
ntt(b);
copy(begin(b), end(b), back_inserter(a));
}
};
#line 5 "ntt/arbitrary-ntt.hpp"
namespace ArbitraryNTT {
using i64 = int64_t;
using u128 = __uint128_t;
constexpr int32_t m0 = 167772161;
constexpr int32_t m1 = 469762049;
constexpr int32_t m2 = 754974721;
using mint0 = LazyMontgomeryModInt<m0>;
using mint1 = LazyMontgomeryModInt<m1>;
using mint2 = LazyMontgomeryModInt<m2>;
constexpr int r01 = mint1(m0).inverse().get();
constexpr int r02 = mint2(m0).inverse().get();
constexpr int r12 = mint2(m1).inverse().get();
constexpr int r02r12 = i64(r02) * r12 % m2;
constexpr i64 w1 = m0;
constexpr i64 w2 = i64(m0) * m1;
template <typename T, typename submint>
vector<submint> mul(const vector<T> &a, const vector<T> &b) {
static NTT<submint> ntt;
vector<submint> s(a.size()), t(b.size());
for (int i = 0; i < (int)a.size(); ++i) s[i] = i64(a[i] % submint::get_mod());
for (int i = 0; i < (int)b.size(); ++i) t[i] = i64(b[i] % submint::get_mod());
return ntt.multiply(s, t);
}
template <typename T>
vector<int> multiply(const vector<T> &s, const vector<T> &t, int mod) {
auto d0 = mul<T, mint0>(s, t);
auto d1 = mul<T, mint1>(s, t);
auto d2 = mul<T, mint2>(s, t);
int n = d0.size();
vector<int> ret(n);
const int W1 = w1 % mod;
const int W2 = w2 % mod;
for (int i = 0; i < n; i++) {
int n1 = d1[i].get(), n2 = d2[i].get(), a = d0[i].get();
int b = i64(n1 + m1 - a) * r01 % m1;
int c = (i64(n2 + m2 - a) * r02r12 + i64(m2 - b) * r12) % m2;
ret[i] = (i64(a) + i64(b) * W1 + i64(c) * W2) % mod;
}
return ret;
}
template <typename mint>
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
if (a.size() == 0 && b.size() == 0) return {};
if (min<int>(a.size(), b.size()) < 128) {
vector<mint> ret(a.size() + b.size() - 1);
for (int i = 0; i < (int)a.size(); ++i)
for (int j = 0; j < (int)b.size(); ++j) ret[i + j] += a[i] * b[j];
return ret;
}
vector<int> s(a.size()), t(b.size());
for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i].get();
for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i].get();
vector<int> u = multiply<int>(s, t, mint::get_mod());
vector<mint> ret(u.size());
for (int i = 0; i < (int)u.size(); ++i) ret[i] = mint(u[i]);
return ret;
}
template <typename T>
vector<u128> multiply_u128(const vector<T> &s, const vector<T> &t) {
if (s.size() == 0 && t.size() == 0) return {};
if (min<int>(s.size(), t.size()) < 128) {
vector<u128> ret(s.size() + t.size() - 1);
for (int i = 0; i < (int)s.size(); ++i)
for (int j = 0; j < (int)t.size(); ++j) ret[i + j] += i64(s[i]) * t[j];
return ret;
}
auto d0 = mul<T, mint0>(s, t);
auto d1 = mul<T, mint1>(s, t);
auto d2 = mul<T, mint2>(s, t);
int n = d0.size();
vector<u128> ret(n);
for (int i = 0; i < n; i++) {
i64 n1 = d1[i].get(), n2 = d2[i].get();
i64 a = d0[i].get();
i64 b = (n1 + m1 - a) * r01 % m1;
i64 c = ((n2 + m2 - a) * r02r12 + (m2 - b) * r12) % m2;
ret[i] = a + b * w1 + u128(c) * w2;
}
return ret;
}
} // namespace ArbitraryNTT
#line 5 "ntt/rader-ntt.hpp"
template <typename mint>
struct RaderNTT {
int p, pr, len;
const vector<mint>& w;
vector<int> prs, iprs;
RaderNTT() {}
RaderNTT(int _p, int _len, const vector<mint>& _w)
: p(_p), pr(constexpr_primitive_root(p)), len(_len), w(_w) {
prs.resize(p - 1);
iprs.resize(p, -1);
for (int i = 0; i < p - 1; i++) prs[i] = i ? prs[i - 1] * pr % p : 1;
for (int i = 0; i < p - 1; i++) iprs[prs[i]] = i;
}
void ntt(vector<mint>& a) {
vector<mint> s(p - 1), t(p - 1);
for (int i = 0; i < p - 1; i++) s[i] = a[prs[i]];
for (int i = 0, ldp = len / p; i < p - 1; i++)
t[i] = w[ldp * prs[i ? p - 1 - i : 0]];
vector<mint> u = ArbitraryNTT::multiply(s, t);
s.resize(p);
fill(begin(s), end(s), a[0]);
for (int i = 1; i < p; i++) s[0] += a[i];
for (int i = 0, y = 0; i < (int)u.size(); i++) {
s[prs[y]] += u[i];
if (--y < 0) y += p - 1;
}
swap(a, s);
}
};
/**
* @brief Rader's FFT Algorithm
*/
#line 4 "ntt/cooley-tukey-ntt.hpp"
template <typename mint>
struct ArbitraryLengthNTT {
using i64 = long long;
int factor(int n) {
for (int i = 2; i * i <= n; i++)
if (n % i == 0) return i;
return n;
}
vector<int> divisor(int n) {
vector<int> ret;
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) {
ret.push_back(i);
ret.push_back(n / i);
}
}
ret.push_back(n);
sort(begin(ret), end(ret));
ret.erase(unique(begin(ret), end(ret)), end(ret));
return ret;
}
int len;
vector<mint> w;
vector<int> divisors;
map<int, RaderNTT<mint> *> rader;
ArbitraryLengthNTT(int len_ = -1) { set_len(len_); }
void set_len(int len_ = -1) {
int mod = mint::get_mod();
if ((len = len_) == -1) len = mod - 1;
if (mod >= 3 && len <= 1) len = 2;
while ((mod - 1) % len != 0) ++len;
mint pr = mint(constexpr_primitive_root(mod)).pow((mod - 1) / len);
w.resize(len + 1);
for (int i = 0; i <= len; i++) w[i] = i ? w[i - 1] * pr : mint(1);
divisors = divisor(len);
}
void dft(vector<mint> &a) {
int N = a.size();
if (N == 2) {
mint a01 = a[0] + a[1];
a[1] = a[0] - a[1];
a[0] = a01;
return;
}
int d = len / N;
vector<mint> b(N);
for (int i = 0, dk = 0; i < N; i++, dk += d) {
for (int j = 0, k = 0; j < N; j++) {
b[j] += a[i] * w[k];
if ((k += dk) >= len) k -= len;
}
}
swap(a, b);
}
void ntt_base2(vector<mint> &a) {
static vector<int> btr;
int N = a.size();
assert(N % 2 == 0);
if (btr.size() != a.size()) {
btr.resize(N);
int b = __builtin_ctz(N);
assert(N == (1 << b));
for (int i = 0; i < N; i++) {
btr[i] = (btr[i >> 1] >> 1) + ((i & 1) << (b - 1));
}
}
static vector<mint> basis;
if (basis.size() < a.size()) {
basis.resize(N);
mint b = w[len / N];
for (int i = N >> 1; i > 0; i >>= 1) {
mint c = 1;
for (int j = 0; j < i; ++j) {
basis[i + j] = c;
c *= b;
}
b *= b;
}
}
for (int i = 0; i < N; i++)
if (i < btr[i]) swap(a[i], a[btr[i]]);
for (int k = 1; k < N; k <<= 1) {
for (int i = 0; i < N; i += 2 * k) {
for (int j = 0; j < k; j++) {
mint z = a[i + j + k] * basis[j + k];
a[i + j + k] = a[i + j] - z;
a[i + j] = a[i + j] + z;
}
}
}
}
void pntt(vector<mint> &a) {
int P = a.size();
if (P <= 64) {
dft(a);
return;
}
if (rader.find(P) == end(rader)) rader[P] = new RaderNTT<mint>(P, len, w);
rader[P]->ntt(a);
}
void ntt(vector<mint> &a) {
assert(len % a.size() == 0);
int N = (int)a.size();
if (N <= 1) return;
if (N <= 64) {
dft(a);
return;
}
int P = factor(N);
if (P == N) {
pntt(a);
return;
}
if (P == 2) {
P = 1 << __builtin_ctz(N);
if (N == P) {
ntt_base2(a);
return;
}
}
int Q = N / P;
vector<mint> t(N), u(P);
{
vector<mint> s(Q);
for (int p = 0, lN = len / N, d = 0; p < P; p++, d += lN) {
for (int q = 0, qP = 0; q < Q; q++, qP += P) s[q] = a[qP + p];
ntt(s);
for (int r = 0, n = 0, pQ = p * Q; r < Q; ++r, n += d) {
t[pQ + r] = w[n] * s[r];
}
}
}
for (int r = 0; r < Q; r++) {
for (int p = 0, pQ = 0; p < P; p++, pQ += Q) u[p] = t[pQ + r];
if (P <= 64)
dft(u);
else if (P & 1)
pntt(u);
else
ntt_base2(u);
for (int s = 0, sQ = 0; s < P; s++, sQ += Q) a[sQ + r] = u[s];
}
}
void intt(vector<mint> &a) {
reverse(begin(a) + 1, end(a));
ntt(a);
mint invn = mint(a.size()).inverse();
for (auto &x : a) x *= invn;
}
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
int N = (int)a.size() + (int)b.size() - 1;
assert(N <= len);
vector<mint> s(a), t(b);
int l = *lower_bound(begin(divisors), end(divisors), N);
s.resize(l, mint(0));
t.resize(l, mint(0));
ntt(s);
ntt(t);
for (int i = 0; i < l; i++) s[i] *= t[i];
intt(s);
s.resize(N);
return s;
}
};
/**
* @brief Cooley-Tukey FFT Algorithm
*/
Cooley-Tukey FFT Algorithm