diff --git a/math/factorial/checker.cpp b/math/factorial/checker.cpp
new file mode 100644
index 000000000..6a66d5330
--- /dev/null
+++ b/math/factorial/checker.cpp
@@ -0,0 +1,62 @@
+// https://github.com/MikeMirzayanov/testlib/blob/master/checkers/wcmp.cpp
+
+// The MIT License (MIT)
+
+// Copyright (c) 2015 Mike Mirzayanov
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "testlib.h"
+
+using namespace std;
+
+int main(int argc, char * argv[])
+{
+    setName("compare sequences of tokens");
+    registerTestlibCmd(argc, argv);
+
+    int n = 0;
+    string j, p;
+
+    while (!ans.seekEof() && !ouf.seekEof()) 
+    {
+        n++;
+
+        ans.readWordTo(j);
+        ouf.readWordTo(p);
+        
+        if (j != p)
+            quitf(_wa, "%d%s words differ - expected: '%s', found: '%s'", n, englishEnding(n).c_str(), compress(j).c_str(), compress(p).c_str());
+    }
+
+    if (ans.seekEof() && ouf.seekEof())
+    {
+        if (n == 1)
+            quitf(_ok, "\"%s\"", compress(j).c_str());
+        else
+            quitf(_ok, "%d tokens", n);
+    }
+    else
+    {
+        if (ans.seekEof())
+            quitf(_wa, "Participant output contains extra tokens");
+        else
+            quitf(_wa, "Unexpected EOF in the participants output");
+    }
+}
diff --git a/math/factorial/gen/example_00.in b/math/factorial/gen/example_00.in
new file mode 100644
index 000000000..a0b2e9a25
--- /dev/null
+++ b/math/factorial/gen/example_00.in
@@ -0,0 +1,6 @@
+5
+0
+5
+100
+1234567
+998244352
diff --git a/math/factorial/gen/near_half.cpp b/math/factorial/gen/near_half.cpp
new file mode 100644
index 000000000..b9318b5a2
--- /dev/null
+++ b/math/factorial/gen/near_half.cpp
@@ -0,0 +1,16 @@
+#include <cstdio>
+#include "../params.h"
+#include "random.h"
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int T = T_MAX;
+  printf("%d\n", T);
+  for (int t = 0; t < T; ++t) {
+    int N = gen.uniform<int>(0.45 * MOD, 0.55 * MOD);
+    printf("%d\n", N);
+  }
+  return 0;
+}
diff --git a/math/factorial/gen/near_max.cpp b/math/factorial/gen/near_max.cpp
new file mode 100644
index 000000000..60232f8cb
--- /dev/null
+++ b/math/factorial/gen/near_max.cpp
@@ -0,0 +1,16 @@
+#include <cstdio>
+#include "../params.h"
+#include "random.h"
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int T = T_MAX;
+  printf("%d\n", T);
+  for (int t = 0; t < T; ++t) {
+    int N = gen.uniform<int>(0.95 * MOD, MOD - 1);
+    printf("%d\n", N);
+  }
+  return 0;
+}
diff --git a/math/factorial/gen/random.cpp b/math/factorial/gen/random.cpp
new file mode 100644
index 000000000..efd579d31
--- /dev/null
+++ b/math/factorial/gen/random.cpp
@@ -0,0 +1,16 @@
+#include <cstdio>
+#include "../params.h"
+#include "random.h"
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int T = T_MAX;
+  printf("%d\n", T);
+  for (int t = 0; t < T; ++t) {
+    int N = gen.uniform<int>(0, MOD - 1);
+    printf("%d\n", N);
+  }
+  return 0;
+}
diff --git a/math/factorial/hash.json b/math/factorial/hash.json
new file mode 100644
index 000000000..cb82cf563
--- /dev/null
+++ b/math/factorial/hash.json
@@ -0,0 +1,16 @@
+{
+  "example_00.in": "180d1bbdde5539dd3a77d325f8940297325665f9f1be249c051dad6aa177200a",
+  "example_00.out": "c73d2af1573bc3649136764834711acaf148eb3588cc639d8bf5a57da9bdd867",
+  "near_half_00.in": "b9b509e96007f2595f9a1845c56544b107a20794261c0a3913056ebc1c472d48",
+  "near_half_00.out": "09c498ab37ca56ec5d94ca104802a0a8fbc78539941f994880463e874cb5e266",
+  "near_half_01.in": "78c59f15afe18136e693628e08aa54d462218ac825d29667c75f5d0e6044babc",
+  "near_half_01.out": "0d58b0459853ec01a08a006ee4f2288c2304264e5551b3a0d65b93dfe111620b",
+  "near_max_00.in": "da530850d58cc2e3e79f6104dc0af91b76a0ec7d61fc5120b4487f2a94312d6f",
+  "near_max_00.out": "06f27a007c8c14ad2cb868844bd5a5e94346dc144ee51b6446a1b684a104902f",
+  "near_max_01.in": "2d4f31d5ddec6a701ed69d204aaa8c49439066f4d675fd99774795757358dc3c",
+  "near_max_01.out": "3655b1fb1215b40a9c762042096ef89af95e7aa94da5ca63b7daf72263c023a1",
+  "random_00.in": "ef2dc732889096480a438e542b5dc79018083e8771651ef8ffa37b0fd1f6c246",
+  "random_00.out": "65ac0924d4ca6ff146997bc802a42aec719d48cc8556127fc2f5d514efaef047",
+  "random_01.in": "0842027f68881d70d3376224a68b92f9e19f13840ef9d573acdba3c85d1fc1d0",
+  "random_01.out": "bd08bbc7d8dd2d279da20ce0ba42d99198728e7b3faccc03ab24c4d5576066f1"
+}
\ No newline at end of file
diff --git a/math/factorial/info.toml b/math/factorial/info.toml
new file mode 100644
index 000000000..656f20d2d
--- /dev/null
+++ b/math/factorial/info.toml
@@ -0,0 +1,26 @@
+title = 'Factorial'
+timelimit = 10.0
+forum = "https://github.com/yosupo06/library-checker-problems/issues/128"
+
+[[tests]]
+    name = "example.in"
+    number = 1
+[[tests]]
+    name = "random.cpp"
+    number = 2
+[[tests]]
+    name = "near_max.cpp"
+    number = 2
+[[tests]]
+    name = "near_half.cpp"
+    number = 2
+
+[[solutions]]
+    name = "naive.cpp"
+    wrong = false
+    allow_tle = true
+
+
+[params]
+    T_MAX = 5
+    MOD = 998244353
diff --git a/math/factorial/sol/correct.cpp b/math/factorial/sol/correct.cpp
new file mode 100644
index 000000000..b11b2df0f
--- /dev/null
+++ b/math/factorial/sol/correct.cpp
@@ -0,0 +1,647 @@
+#include <cstdio>
+#include <vector>
+#include <cassert>
+#include <array>
+
+using namespace std;
+
+using ll = long long;
+using u32 = unsigned int;
+using u64 = unsigned long long;
+using u128 = unsigned __int128;
+
+using pi = pair<ll, ll>;
+using vi = vector<ll>;
+template <class T>
+using vc = vector<T>;
+template <class T>
+using vvc = vector<vc<T>>;
+template <class T>
+using vvvc = vector<vvc<T>>;
+#define vv(type, name, h, ...) \
+  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
+#define vvv(type, name, h, w, ...)   \
+  vector<vector<vector<type>>> name( \
+      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
+
+#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
+#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
+#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
+#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
+#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
+#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
+#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
+#define overload4(a, b, c, d, e, ...) e
+#define overload3(a, b, c, d, ...) d
+#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
+#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
+
+#define all(x) x.begin(), x.end()
+#define len(x) ll(x.size())
+#define elif else if
+
+#define eb emplace_back
+#define mp make_pair
+#define mt make_tuple
+#define fi first
+#define se second
+
+// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
+int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
+int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
+int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
+int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
+
+template <typename mint>
+mint inv(int n) {
+  static const int mod = mint::get_mod();
+  static vector<mint> dat = {0, 1};
+  assert(0 <= n);
+  if (n >= mod) n %= mod;
+  while (len(dat) <= n) {
+    int k = len(dat);
+    int q = (mod + k - 1) / k;
+    dat.eb(dat[k * q - mod] * mint::raw(q));
+  }
+  return dat[n];
+}
+
+template <typename mint>
+mint fact(int n) {
+  static const int mod = mint::get_mod();
+  assert(0 <= n && n < mod);
+  static vector<mint> dat = {1, 1};
+  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
+  return dat[n];
+}
+
+template <typename mint>
+mint fact_inv(int n) {
+  static vector<mint> dat = {1, 1};
+  if (n < 0) return mint(0);
+  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
+  return dat[n];
+}
+
+template <class mint, class... Ts>
+mint fact_invs(Ts... xs) {
+  return (mint(1) * ... * fact_inv<mint>(xs));
+}
+
+template <int mod>
+struct modint {
+  static constexpr u32 umod = u32(mod);
+  static_assert(umod < u32(1) << 31);
+  u32 val;
+
+  static modint raw(u32 v) {
+    modint x;
+    x.val = v;
+    return x;
+  }
+  constexpr modint() : val(0) {}
+  constexpr modint(u32 x) : val(x % umod) {}
+  constexpr modint(u64 x) : val(x % umod) {}
+  constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
+  constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
+  bool operator<(const modint &other) const { return val < other.val; }
+  modint &operator+=(const modint &p) {
+    if ((val += p.val) >= umod) val -= umod;
+    return *this;
+  }
+  modint &operator-=(const modint &p) {
+    if ((val += umod - p.val) >= umod) val -= umod;
+    return *this;
+  }
+  modint &operator*=(const modint &p) {
+    val = u64(val) * p.val % umod;
+    return *this;
+  }
+  modint &operator/=(const modint &p) {
+    *this *= p.inverse();
+    return *this;
+  }
+  modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
+  modint operator+(const modint &p) const { return modint(*this) += p; }
+  modint operator-(const modint &p) const { return modint(*this) -= p; }
+  modint operator*(const modint &p) const { return modint(*this) *= p; }
+  modint operator/(const modint &p) const { return modint(*this) /= p; }
+  bool operator==(const modint &p) const { return val == p.val; }
+  bool operator!=(const modint &p) const { return val != p.val; }
+  modint inverse() const {
+    int a = val, b = mod, u = 1, v = 0, t;
+    while (b > 0) {
+      t = a / b;
+      swap(a -= t * b, b), swap(u -= t * v, v);
+    }
+    return modint(u);
+  }
+  modint pow(ll n) const {
+    assert(n >= 0);
+    modint ret(1), mul(val);
+    while (n > 0) {
+      if (n & 1) ret *= mul;
+      mul *= mul;
+      n >>= 1;
+    }
+    return ret;
+  }
+  static constexpr int get_mod() { return mod; }
+  // (n, r), r は 1 の 2^n 乗根
+  static constexpr pair<int, int> ntt_info() {
+    if (mod == 167772161) return {25, 17};
+    if (mod == 469762049) return {26, 30};
+    if (mod == 754974721) return {24, 362};
+    if (mod == 880803841) return {23, 211};
+    if (mod == 943718401) return {22, 663003469};
+    if (mod == 998244353) return {23, 31};
+    if (mod == 1045430273) return {20, 363};
+    if (mod == 1051721729) return {20, 330};
+    if (mod == 1053818881) return {20, 2789};
+    return {-1, -1};
+  }
+  static constexpr bool can_ntt() { return ntt_info().fi != -1; }
+};
+
+using modint998 = modint<998244353>;
+
+template <class T>
+vc<vc<T>> matrix_mul(const vc<vc<T>> &A, const vc<vc<T>> &B, int N1 = -1,
+                     int N2 = -1, int N3 = -1) {
+  if (N1 == -1) { N1 = len(A), N2 = len(B), N3 = len(B[0]); }
+  vv(u32, b, N3, N2);
+  FOR(i, N2) FOR(j, N3) b[j][i] = B[i][j].val;
+  vv(T, C, N1, N3);
+
+  if ((T::get_mod() < (1 << 30)) && N2 <= 16) {
+    FOR(i, N1) FOR(j, N3) {
+      u64 sm = 0;
+      FOR(m, N2) sm += u64(A[i][m].val) * b[j][m];
+      C[i][j] = sm;
+    }
+  } else {
+    FOR(i, N1) FOR(j, N3) {
+      u128 sm = 0;
+      FOR(m, N2) sm += u64(A[i][m].val) * b[j][m];
+      C[i][j] = T::raw(sm % (T::get_mod()));
+    }
+  }
+  return C;
+}
+
+template <class T>
+struct Monoid_Mul {
+  using value_type = T;
+  using X = T;
+  static constexpr X op(const X &x, const X &y) noexcept { return x * y; }
+  static constexpr X inverse(const X &x) noexcept { return X(1) / x; }
+  static constexpr X unit() { return X(1); }
+  static constexpr bool commute = true;
+};
+
+template <class Monoid>
+struct Sliding_Window_Aggregation {
+  using X = typename Monoid::value_type;
+  using value_type = X;
+  int sz = 0;
+  vc<X> dat;
+  vc<X> cum_l;
+  X cum_r;
+
+  Sliding_Window_Aggregation()
+      : cum_l({Monoid::unit()}), cum_r(Monoid::unit()) {}
+
+  int size() { return sz; }
+
+  void push(X x) {
+    ++sz;
+    cum_r = Monoid::op(cum_r, x);
+    dat.eb(x);
+  }
+
+  void pop() {
+    --sz;
+    cum_l.pop_back();
+    if (len(cum_l) == 0) {
+      cum_l = {Monoid::unit()};
+      cum_r = Monoid::unit();
+      while (len(dat) > 1) {
+        cum_l.eb(Monoid::op(dat.back(), cum_l.back()));
+        dat.pop_back();
+      }
+      dat.pop_back();
+    }
+  }
+
+  X lprod() { return cum_l.back(); }
+  X rprod() { return cum_r; }
+
+  X prod() { return Monoid::op(cum_l.back(), cum_r); }
+};
+
+// long でも大丈夫
+// (val * x - 1) が mod の倍数になるようにする
+// 特に mod=0 なら x=0 が満たす
+ll mod_inv(ll val, ll mod) {
+  assert(mod >= 0);
+  if (mod == 0) return 0;
+  val %= mod;
+  if (val < 0) val += mod;
+  ll a = val, b = mod, u = 1, v = 0, t;
+  while (b > 0) {
+    t = a / b;
+    swap(a -= t * b, b), swap(u -= t * v, v);
+  }
+  if (u < 0) u += mod;
+  return u;
+}
+#line 1 "library/mod/crt3.hpp"
+
+constexpr u32 mod_pow_constexpr(u64 a, u64 n, u32 mod) {
+  a %= mod;
+  u64 res = 1;
+  FOR(32) {
+    if (n & 1) res = res * a % mod;
+    a = a * a % mod, n /= 2;
+  }
+  return res;
+}
+
+template <typename T, u32 p0, u32 p1, u32 p2>
+T CRT3(u64 a0, u64 a1, u64 a2) {
+  static_assert(p0 < p1 && p1 < p2);
+  static constexpr u64 x0_1 = mod_pow_constexpr(p0, p1 - 2, p1);
+  static constexpr u64 x01_2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);
+  u64 c = (a1 - a0 + p1) * x0_1 % p1;
+  u64 a = a0 + c * p0;
+  c = (a2 - a % p2 + p2) * x01_2 % p2;
+  return T(a) + T(c) * T(p0) * T(p1);
+}
+#line 2 "library/poly/convolution_naive.hpp"
+
+template <class T>
+vc<T> convolution_naive(const vc<T> &a, const vc<T> &b) {
+  int n = int(a.size()), m = int(b.size());
+  if (n > m) return convolution_naive<T>(b, a);
+  if (n == 0) return {};
+  vc<T> ans(n + m - 1);
+  if (n <= 16 && (T::get_mod() < (1 << 30))) {
+    for (int k = 0; k < n + m - 1; ++k) {
+      int s = max(0, k - m + 1);
+      int t = min(n, k + 1);
+      u64 sm = 0;
+      for (int i = s; i < t; ++i) { sm += u64(a[i].val) * (b[k - i].val); }
+      ans[k] = sm;
+    }
+  } else {
+    for (int k = 0; k < n + m - 1; ++k) {
+      int s = max(0, k - m + 1);
+      int t = min(n, k + 1);
+      u128 sm = 0;
+      for (int i = s; i < t; ++i) { sm += u64(a[i].val) * (b[k - i].val); }
+      ans[k] = T::raw(sm % T::get_mod());
+    }
+  }
+  return ans;
+}
+
+template <typename T>
+vc<T> convolution_karatsuba(const vc<T> &f, const vc<T> &g) {
+  const int thresh = 30;
+  if (min(len(f), len(g)) <= thresh) return convolution_naive(f, g);
+  int n = max(len(f), len(g));
+  int m = (n + 1) / 2;
+  vc<T> f1, f2, g1, g2;
+  if (len(f) < m) f1 = f;
+  if (len(f) >= m) f1 = {f.begin(), f.begin() + m};
+  if (len(f) >= m) f2 = {f.begin() + m, f.end()};
+  if (len(g) < m) g1 = g;
+  if (len(g) >= m) g1 = {g.begin(), g.begin() + m};
+  if (len(g) >= m) g2 = {g.begin() + m, g.end()};
+  vc<T> a = convolution_karatsuba(f1, g1);
+  vc<T> b = convolution_karatsuba(f2, g2);
+  FOR(i, len(f2)) f1[i] += f2[i];
+  FOR(i, len(g2)) g1[i] += g2[i];
+  vc<T> c = convolution_karatsuba(f1, g1);
+  vc<T> F(len(f) + len(g) - 1);
+  assert(2 * m + len(b) <= len(F));
+  FOR(i, len(a)) F[i] += a[i], c[i] -= a[i];
+  FOR(i, len(b)) F[2 * m + i] += b[i], c[i] -= b[i];
+  if (c.back() == T(0)) c.pop_back();
+  FOR(i, len(c)) if (c[i] != T(0)) F[m + i] += c[i];
+  return F;
+}
+
+template <class mint>
+void ntt(vector<mint> &a, bool inverse) {
+  assert(mint::can_ntt());
+  const int rank2 = mint::ntt_info().fi;
+  const int mod = mint::get_mod();
+  static array<mint, 30> root, iroot;
+  static array<mint, 30> rate2, irate2;
+  static array<mint, 30> rate3, irate3;
+
+  static bool prepared = 0;
+  if (!prepared) {
+    prepared = 1;
+    root[rank2] = mint::ntt_info().se;
+    iroot[rank2] = mint(1) / root[rank2];
+    FOR_R(i, rank2) {
+      root[i] = root[i + 1] * root[i + 1];
+      iroot[i] = iroot[i + 1] * iroot[i + 1];
+    }
+    mint prod = 1, iprod = 1;
+    for (int i = 0; i <= rank2 - 2; i++) {
+      rate2[i] = root[i + 2] * prod;
+      irate2[i] = iroot[i + 2] * iprod;
+      prod *= iroot[i + 2];
+      iprod *= root[i + 2];
+    }
+    prod = 1, iprod = 1;
+    for (int i = 0; i <= rank2 - 3; i++) {
+      rate3[i] = root[i + 3] * prod;
+      irate3[i] = iroot[i + 3] * iprod;
+      prod *= iroot[i + 3];
+      iprod *= root[i + 3];
+    }
+  }
+
+  int n = int(a.size());
+  int h = topbit(n);
+  assert(n == 1 << h);
+  if (!inverse) {
+    int len = 0;
+    while (len < h) {
+      if (h - len == 1) {
+        int p = 1 << (h - len - 1);
+        mint rot = 1;
+        FOR(s, 1 << len) {
+          int offset = s << (h - len);
+          FOR(i, p) {
+            auto l = a[i + offset];
+            auto r = a[i + offset + p] * rot;
+            a[i + offset] = l + r;
+            a[i + offset + p] = l - r;
+          }
+          rot *= rate2[topbit(~s & -~s)];
+        }
+        len++;
+      } else {
+        int p = 1 << (h - len - 2);
+        mint rot = 1, imag = root[2];
+        for (int s = 0; s < (1 << len); s++) {
+          mint rot2 = rot * rot;
+          mint rot3 = rot2 * rot;
+          int offset = s << (h - len);
+          for (int i = 0; i < p; i++) {
+            u64 mod2 = u64(mod) * mod;
+            u64 a0 = a[i + offset].val;
+            u64 a1 = u64(a[i + offset + p].val) * rot.val;
+            u64 a2 = u64(a[i + offset + 2 * p].val) * rot2.val;
+            u64 a3 = u64(a[i + offset + 3 * p].val) * rot3.val;
+            u64 a1na3imag = (a1 + mod2 - a3) % mod * imag.val;
+            u64 na2 = mod2 - a2;
+            a[i + offset] = a0 + a2 + a1 + a3;
+            a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
+            a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
+            a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
+          }
+          rot *= rate3[topbit(~s & -~s)];
+        }
+        len += 2;
+      }
+    }
+  } else {
+    mint coef = mint(1) / mint(len(a));
+    FOR(i, len(a)) a[i] *= coef;
+    int len = h;
+    while (len) {
+      if (len == 1) {
+        int p = 1 << (h - len);
+        mint irot = 1;
+        FOR(s, 1 << (len - 1)) {
+          int offset = s << (h - len + 1);
+          FOR(i, p) {
+            u64 l = a[i + offset].val;
+            u64 r = a[i + offset + p].val;
+            a[i + offset] = l + r;
+            a[i + offset + p] = (mod + l - r) * irot.val;
+          }
+          irot *= irate2[topbit(~s & -~s)];
+        }
+        len--;
+      } else {
+        int p = 1 << (h - len);
+        mint irot = 1, iimag = iroot[2];
+        FOR(s, (1 << (len - 2))) {
+          mint irot2 = irot * irot;
+          mint irot3 = irot2 * irot;
+          int offset = s << (h - len + 2);
+          for (int i = 0; i < p; i++) {
+            u64 a0 = a[i + offset + 0 * p].val;
+            u64 a1 = a[i + offset + 1 * p].val;
+            u64 a2 = a[i + offset + 2 * p].val;
+            u64 a3 = a[i + offset + 3 * p].val;
+            u64 x = (mod + a2 - a3) * iimag.val % mod;
+            a[i + offset] = a0 + a1 + a2 + a3;
+            a[i + offset + 1 * p] = (a0 + mod - a1 + x) * irot.val;
+            a[i + offset + 2 * p] = (a0 + a1 + 2 * mod - a2 - a3) * irot2.val;
+            a[i + offset + 3 * p] = (a0 + 2 * mod - a1 - x) * irot3.val;
+          }
+          irot *= irate3[topbit(~s & -~s)];
+        }
+        len -= 2;
+      }
+    }
+  }
+}
+
+template <class mint>
+vector<mint> convolution_ntt(vector<mint> a, vector<mint> b) {
+  if (a.empty() || b.empty()) return {};
+  int n = int(a.size()), m = int(b.size());
+  int sz = 1;
+  while (sz < n + m - 1) sz *= 2;
+
+  // sz = 2^k のときの高速化。分割統治的なやつで損しまくるので。
+  if ((n + m - 3) <= sz / 2) {
+    auto a_last = a.back(), b_last = b.back();
+    a.pop_back(), b.pop_back();
+    auto c = convolution(a, b);
+    c.resize(n + m - 1);
+    c[n + m - 2] = a_last * b_last;
+    FOR(i, len(a)) c[i + len(b)] += a[i] * b_last;
+    FOR(i, len(b)) c[i + len(a)] += b[i] * a_last;
+    return c;
+  }
+
+  a.resize(sz), b.resize(sz);
+  bool same = a == b;
+  ntt(a, 0);
+  if (same) {
+    b = a;
+  } else {
+    ntt(b, 0);
+  }
+  FOR(i, sz) a[i] *= b[i];
+  ntt(a, 1);
+  a.resize(n + m - 1);
+  return a;
+}
+
+template <typename mint>
+vc<mint> convolution(const vc<mint> &a, const vc<mint> &b) {
+  int n = len(a), m = len(b);
+  if (!n || !m) return {};
+  if (min(n, m) <= 50) return convolution_karatsuba<mint>(a, b);
+  return convolution_ntt(a, b);
+}
+
+// Input: f(0), ..., f(n-1) and c. Return: f(c)
+template <typename T>
+T lagrange_interpolate_iota(vc<T> &f, T c) {
+  int n = len(f);
+  if (int(c.val) < n) return f[c.val];
+  auto a = f;
+  FOR(i, n) {
+    a[i] = a[i] * fact_inv<T>(i) * fact_inv<T>(n - 1 - i);
+    if ((n - 1 - i) & 1) a[i] = -a[i];
+  }
+  vc<T> lp(n + 1), rp(n + 1);
+  lp[0] = rp[n] = 1;
+  FOR(i, n) lp[i + 1] = lp[i] * (c - i);
+  FOR_R(i, n) rp[i] = rp[i + 1] * (c - i);
+  T ANS = 0;
+  FOR(i, n) ANS += a[i] * lp[i] * rp[i + 1];
+  return ANS;
+}
+
+// Input: f(0), ..., f(n-1) and c, m
+// Return: f(c), f(c+1), ..., f(c+m-1)
+// Complexity: M(n, n + m)
+template <typename mint>
+vc<mint> lagrange_interpolate_iota(vc<mint> &f, mint c, int m) {
+  if (m <= 60) {
+    vc<mint> ANS(m);
+    FOR(i, m) ANS[i] = lagrange_interpolate_iota(f, c + mint(i));
+    return ANS;
+  }
+  ll n = len(f);
+  auto a = f;
+  FOR(i, n) {
+    a[i] = a[i] * fact_inv<mint>(i) * fact_inv<mint>(n - 1 - i);
+    if ((n - 1 - i) & 1) a[i] = -a[i];
+  }
+  // x = c, c+1, ... に対して a0/x + a1/(x-1) + ... を求めておく
+  vc<mint> b(n + m - 1);
+  FOR(i, n + m - 1) b[i] = mint(1) / (c + mint(i - n + 1));
+  a = convolution(a, b);
+
+  Sliding_Window_Aggregation<Monoid_Mul<mint>> swag;
+  vc<mint> ANS(m);
+  ll L = 0, R = 0;
+  FOR(i, m) {
+    while (L < i) { swag.pop(), ++L; }
+    while (R - L < n) { swag.push(c + mint((R++) - n + 1)); }
+    auto coef = swag.prod();
+    if (coef == 0) {
+      ANS[i] = f[(c + i).val];
+    } else {
+      ANS[i] = a[i + n - 1] * coef;
+    }
+  }
+  return ANS;
+}
+
+template <typename T>
+vc<vc<T>> prefix_product_of_poly_matrix(vc<vc<vc<T>>> &A, ll k) {
+  int n = len(A);
+
+  using MAT = vc<vc<T>>;
+  auto shift = [&](vc<MAT> &G, T x) -> vc<MAT> {
+    int d = len(G);
+    vvv(T, H, d, n, n);
+    FOR(i, n) FOR(j, n) {
+      vc<T> g(d);
+      FOR(l, d) g[l] = G[l][i][j];
+      auto h = lagrange_interpolate_iota(g, x, d);
+      FOR(l, d) H[l][i][j] = h[l];
+    }
+    return H;
+  };
+
+  auto evaluate = [&](vc<T> &f, T x) -> T {
+    T res = 0;
+    T p = 1;
+    FOR(i, len(f)) {
+      res += f[i] * p;
+      p *= x;
+    }
+    return res;
+  };
+
+  ll deg = 1;
+  FOR(i, n) FOR(j, n) deg = max(deg, len(A[i][j]) - 1);
+
+  vc<MAT> G(deg + 1);
+  ll v = 1;
+  while (deg * v * v < k) v *= 2;
+  T iv = T(1) / T(v);
+
+  FOR(i, len(G)) {
+    T x = T(v) * T(i);
+    vv(T, mat, n, n);
+    FOR(j, n) FOR(k, n) mat[j][k] = evaluate(A[j][k], x);
+    G[i] = mat;
+  }
+
+  for (ll w = 1; w != v; w *= 2) {
+    T W = w;
+    auto G1 = shift(G, W * iv);
+    auto G2 = shift(G, (W * T(deg) * T(v) + T(v)) * iv);
+    auto G3 = shift(G, (W * T(deg) * T(v) + T(v) + W) * iv);
+    FOR(i, w * deg + 1) {
+      G[i] = matrix_mul(G1[i], G[i]);
+      G2[i] = matrix_mul(G3[i], G2[i]);
+    }
+    copy(G2.begin(), G2.end() - 1, back_inserter(G));
+  }
+
+  vv(T, res, n, n);
+  FOR(i, n) res[i][i] = 1;
+  ll i = 0;
+  while (i + v <= k) res = matrix_mul(G[i / v], res), i += v;
+  while (i < k) {
+    vv(T, mat, n, n);
+    FOR(j, n) FOR(k, n) mat[j][k] = evaluate(A[j][k], i);
+    res = matrix_mul(mat, res);
+    ++i;
+  }
+  return res;
+}
+
+template <typename T>
+T prefix_product_of_poly(vc<T> &f, ll k) {
+  vc<vc<vc<T>>> A(1);
+  A[0].resize(1);
+  A[0][0] = f;
+  auto res = prefix_product_of_poly_matrix(A, k);
+  return res[0][0];
+}
+
+using mint = modint998;
+
+void solve() {
+  int N;
+  scanf("%d", &N);
+  vc<mint> f = {1, 1};
+  mint b = prefix_product_of_poly(f, N);
+  printf("%d\n", b.val);
+}
+
+signed main() {
+  int T;
+  scanf("%d", &T);
+  for (int t = 0; t < T; ++t) solve();
+  return 0;
+}
diff --git a/math/factorial/sol/naive.cpp b/math/factorial/sol/naive.cpp
new file mode 100644
index 000000000..8cee4078a
--- /dev/null
+++ b/math/factorial/sol/naive.cpp
@@ -0,0 +1,35 @@
+#include <cstdio>
+
+using namespace std;
+
+constexpr int mod = 998244353;
+
+void solve() {
+  int N;
+  scanf("%d", &N);
+  if (N < mod / 2) {
+    long long x = 1;
+    for (int n = 1; n <= N; ++n) x = x * n % mod;
+    printf("%lld\n", x);
+  } else {
+    long long x = mod - 1; // (mod-1)!
+    long long y = 1;
+    for (int n = N + 1; n <= mod - 1; ++n) { y = y * n % mod; }
+    // x / y
+    // xy^{mod-2}
+    long long n = mod - 2;
+    while (n) {
+      if (n & 1) x = x * y % mod;
+      y = y * y % mod;
+      n /= 2;
+    }
+    printf("%lld\n", x);
+  }
+}
+
+signed main() {
+  int T;
+  scanf("%d", &T);
+  for (int t = 0; t < T; ++t) solve();
+  return 0;
+}
diff --git a/math/factorial/task.md b/math/factorial/task.md
new file mode 100644
index 000000000..cbfdaa7ab
--- /dev/null
+++ b/math/factorial/task.md
@@ -0,0 +1,41 @@
+## @{keyword.statement}
+
+@{lang.en}
+
+This problem has $T$ cases.
+
+Given a non-negative integer $N$. Print $N!$ modulo $@{param.MOD}$. 
+
+@{lang.ja}
+
+この問題は $T$ ケースあります．
+非負整数 $N$ が与えられます．$N!$ を $@{param.MOD}$ で割った余りを出力してください．
+
+@{lang.end}
+
+## @{keyword.constraints}
+
+- $1\leq T\leq 5$
+- $0 \leq N < @{param.MOD}$
+
+## @{keyword.input}
+
+```
+$T$
+$N_1$
+$\vdots$
+$N_T$
+```
+
+## @{keyword.output}
+@{lang.en}
+Print $N!$ modulo $@{param.MOD}$. 
+
+@{lang.ja}
+
+$N!$ を $@{param.MOD}$ で割った余りを出力してください．
+@{lang.end}
+
+## @{keyword.sample}
+
+@{example.example_00}
diff --git a/math/factorial/verifier.cpp b/math/factorial/verifier.cpp
new file mode 100644
index 000000000..cbd5d79bf
--- /dev/null
+++ b/math/factorial/verifier.cpp
@@ -0,0 +1,15 @@
+#include <iostream>
+#include "params.h"
+#include "testlib.h"
+
+int main() {
+  registerValidation();
+  int T = inf.readInt(1, T_MAX);
+  inf.readChar('\n');
+  for (int t = 0; t < T; ++t) {
+    inf.readLong(0, MOD - 1);
+    inf.readChar('\n');
+  }
+  inf.readEof();
+  return 0;
+}