Problem p03009 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;
// #define int long long
#define REP(i, n) for (int i = 0, max_i = (n); i < max_i; i++)
#define REPI(i, a, b) for (int i = (a), max_i = (b); i < max_i; i++)
#define ALL(obj) begin(obj), end(obj)
#define RALL(obj) rbegin(obj), rend(obj)
#define fi first
#define se second
using ii = pair<int, int>;
vector<ii> dirs = {
    {1, 0}, {0, 1},  {-1, 0},  {0, -1}, // 4方向
    {1, 1}, {-1, 1}, {-1, -1}, {1, -1}, // 斜め
    {0, 0},                             // 自身
};
template <class T> inline bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T, class S> vector<T> make_vec(size_t n, S x) {
  return vector<T>(n, x);
}
template <class T, class... Ts> auto make_vec(size_t n, Ts... ts) {
  return vector<decltype(make_vec<T>(ts...))>(n, make_vec<T>(ts...));
}

// debug
template <class T> ostream &operator<<(ostream &s, vector<T> &d) {
  REP(i, d.size()) s << d[i] << (i == d.size() - 1 ? "" : " ");
  return s;
}
template <class T> ostream &operator<<(ostream &s, vector<vector<T>> &d) {
  REP(i, d.size()) s << d[i] << (i == d.size() - 1 ? "" : "\n");
  return s;
}
template <class T, class S> ostream &operator<<(ostream &s, pair<T, S> &p) {
  s << "{" << p.first << ", " << p.second << "}";
  return s;
}
template <class T, class S> ostream &operator<<(ostream &s, map<T, S> m) {
  for (auto it = m.begin(); it != m.end(); it++) {
    s << *it << (next(it) == m.end() ? "" : "\n");
  }
  return s;
}
template <class T, class S>
ostream &operator<<(ostream &s, unordered_map<T, S> m) {
  for (auto it = m.begin(); it != m.end(); it++) {
    s << *it << (next(it) == m.end() ? "" : "\n");
  }
  return s;
}
#ifdef _MY_DEBUG
#define dump(...)                                                              \
  cerr << "/* " << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__    \
       << "]" << endl,                                                         \
      dump_func(__VA_ARGS__), cerr << "*/\n\n";
#else
#define dump(...)
#define endl "\n"
#endif
void dump_func() { cerr << endl; }
template <class Head, class... Tail> void dump_func(Head &&h, Tail &&...t) {
  cerr << h << (sizeof...(Tail) == 0 ? "" : ", "),
      dump_func(forward<Tail>(t)...);
}

struct Fast {
  Fast() {
    cin.tie(0);
    ios::sync_with_stdio(false);
  }
} fast;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
constexpr int MOD = 1000000007;
// *************** TEMPLATE END ***************

template <class T> T pow(T x, int n, const T UNION = 1) {
  T ret = UNION;
  while (n) {
    if (n & 1)
      ret *= x;
    x *= x;
    n >>= 1;
  }
  return ret;
}

template <int MD> struct ModInt {
  int x;
  static unordered_map<int, int> to_inv;
  ModInt() : x(0) {}
  ModInt(int x_) {
    if ((x = x_ % MD + MD) >= MD)
      x -= MD;
  }

  ModInt &operator+=(ModInt that) {
    if ((x += that.x) >= MD)
      x -= MD;
    return *this;
  }
  ModInt &operator*=(ModInt that) {
    x = (unsigned long long)x * that.x % MD;
    return *this;
  }
  ModInt &operator-=(ModInt that) {
    if ((x -= that.x) < 0)
      x += MD;
    return *this;
  }
  ModInt &operator/=(ModInt that) {
    x = (unsigned long long)x * that.inv().x % MD;
    return *this;
  }

  ModInt operator-() const { return -x < 0 ? MD - x : -x; }
  ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
  ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
  ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
  ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }
  bool operator==(ModInt that) const { return x == that.x; }
  bool operator!=(ModInt that) const { return x != that.x; }
  ModInt inv() const {
    return to_inv.count(this->x) ? to_inv[this->x]
                                 : (to_inv[this->x] = pow(*this, MD - 2).x);
  }
  friend ostream &operator<<(ostream &s, ModInt<MD> a) {
    s << a.x;
    return s;
  }
  friend istream &operator>>(istream &s, ModInt<MD> &a) {
    s >> a.x;
    return s;
  }
};
template <int MD> unordered_map<int, int> ModInt<MD>::to_inv;
using mint = ModInt<MOD>;

vector<mint> fact, fact_inv;
void init_factorial(int n) {
  fact = vector<mint>(n + 1, 1);
  fact_inv = vector<mint>(n + 1);
  for (int i = 0; i < n; i++)
    fact[i + 1] = fact[i] * (i + 1);
  fact_inv[n] = mint(1) / fact[n];
  for (int i = n - 1; i >= 0; i--)
    fact_inv[i] = fact_inv[i + 1] * (i + 1);
  // for (int i = 0; i < n + 1; i++) assert(fact[i] * fact_inv[i] == 1);
}
mint comb(int n, int r) { return fact[n] * fact_inv[r] * fact_inv[n - r]; }

// T0: 元の配列のモノイド
// T1: T0に対する作用素モノイド
template <class T0, class T1> class SegmentTree {
  // k番目のノードにのlazyを伝搬
  void eval(int k, int len) {
    // u1が正確に単位元ならいらない
    // if (lazy[k] == u1) return;
    // len個分のlazy[k]を評価
    node[k] = g(node[k], p(lazy[k], len));
    if (k < N - 1) {
      // 最下段でなければ下のlazyに伝搬
      lazy[2 * k + 1] = f1(lazy[2 * k + 1], lazy[k]);
      lazy[2 * k + 2] = f1(lazy[2 * k + 2], lazy[k]);
    }
    lazy[k] = u1;
  }
  // k番目のノード[l, r)について、[a, b)の範囲内にxを作用
  void update(int a, int b, T1 x, int k, int l, int r) {
    eval(k, r - l);
    if (b <= l || r <= a)
      return;
    if (a <= l && r <= b) {
      lazy[k] = f1(lazy[k], x);
      eval(k, r - l);
    } else {
      update(a, b, x, 2 * k + 1, l, (l + r) / 2);
      update(a, b, x, 2 * k + 2, (l + r) / 2, r);
      node[k] = f0(node[2 * k + 1], node[2 * k + 2]);
    }
  }
  // k番目のノード[l, r)について、[a, b)のクエリを求める
  T0 query(int a, int b, int k, int l, int r) {
    if (r <= a || b <= l)
      return u0;
    eval(k, r - l);
    if (a <= l && r <= b)
      return node[k];
    T0 vl = query(a, b, 2 * k + 1, l, (l + r) / 2);
    T0 vr = query(a, b, 2 * k + 2, (l + r) / 2, r);
    return f0(vl, vr);
  }

public:
  int sz; // 元の配列のサイズ
  int N;
  vector<T0> node;
  vector<T1> lazy;
  // T0上の演算、単位元
  using F0 = function<T0(T0, T0)>;
  F0 f0;
  T0 u0;
  // T1上の演算、単位元
  using F1 = function<T1(T1, T1)>;
  F1 f1;
  T1 u1;
  // 作用
  using G = function<T0(T0, T1)>;
  G g;
  // 多数のt1(T1)に対するf1の合成
  using P = function<T1(T1, int)>;
  P p;
  SegmentTree(const vector<T0> &a, F0 f0, T0 u0, F1 f1, T1 u1, G g, P p)
      : sz(a.size()), f0(f0), u0(u0), f1(f1), u1(u1), g(g), p(p) {
    for (N = 1; N < sz; N *= 2)
      ;
    node.resize(2 * N - 1);
    lazy.resize(2 * N - 1, u1);
    REP(i, sz) node[N - 1 + i] = a[i];
    for (int i = N - 2; i >= 0; i--)
      node[i] = f0(node[2 * i + 1], node[2 * i + 2]);
  }
  // [a, b)にxを作用
  void update(int a, int b, T1 x) {
    assert(0 <= a && a < b && b <= sz);
    update(a, b, x, 0, 0, N);
  }
  void update(int a, T1 x) { update(a, a + 1, x); }
  // [a, b)
  T0 query(int a, int b) { return query(a, b, 0, 0, N); }
  T0 query(int a) { return query(a, a + 1); }
};

signed main() {
  int n, H, D;
  cin >> n >> H >> D;
  init_factorial(n + 10);
  mint mul = 0;
  REPI(i, 1, n + 1) { mul += fact[i]; }

  // Sum & Add
  SegmentTree<mint, mint> seg(vector<mint>(H + 1, 0), plus<mint>(), 0,
                              plus<mint>(), 0, plus<mint>(),
                              multiplies<mint>());
  seg.update(0, fact[n] / mul);
  REP(i, H) {
    mint now = seg.query(i);
    seg.update(i + 1, min(H + 1, i + D + 1), now * mul);
  }
  cout << seg.query(H) << endl;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
// #define int long long
#define REP(i, n) for (int i = 0, max_i = (n); i < max_i; i++)
#define REPI(i, a, b) for (int i = (a), max_i = (b); i < max_i; i++)
#define ALL(obj) begin(obj), end(obj)
#define RALL(obj) rbegin(obj), rend(obj)
#define fi first
#define se second
using ii = pair<int, int>;
vector<ii> dirs = {
    {1, 0}, {0, 1},  {-1, 0},  {0, -1}, // 4方向
    {1, 1}, {-1, 1}, {-1, -1}, {1, -1}, // 斜め
    {0, 0},                             // 自身
};
template <class T> inline bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T, class S> vector<T> make_vec(size_t n, S x) {
  return vector<T>(n, x);
}
template <class T, class... Ts> auto make_vec(size_t n, Ts... ts) {
  return vector<decltype(make_vec<T>(ts...))>(n, make_vec<T>(ts...));
}

// debug
template <class T> ostream &operator<<(ostream &s, vector<T> &d) {
  REP(i, d.size()) s << d[i] << (i == d.size() - 1 ? "" : " ");
  return s;
}
template <class T> ostream &operator<<(ostream &s, vector<vector<T>> &d) {
  REP(i, d.size()) s << d[i] << (i == d.size() - 1 ? "" : "\n");
  return s;
}
template <class T, class S> ostream &operator<<(ostream &s, pair<T, S> &p) {
  s << "{" << p.first << ", " << p.second << "}";
  return s;
}
template <class T, class S> ostream &operator<<(ostream &s, map<T, S> m) {
  for (auto it = m.begin(); it != m.end(); it++) {
    s << *it << (next(it) == m.end() ? "" : "\n");
  }
  return s;
}
template <class T, class S>
ostream &operator<<(ostream &s, unordered_map<T, S> m) {
  for (auto it = m.begin(); it != m.end(); it++) {
    s << *it << (next(it) == m.end() ? "" : "\n");
  }
  return s;
}
#ifdef _MY_DEBUG
#define dump(...)                                                              \
  cerr << "/* " << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__    \
       << "]" << endl,                                                         \
      dump_func(__VA_ARGS__), cerr << "*/\n\n";
#else
#define dump(...)
#define endl "\n"
#endif
void dump_func() { cerr << endl; }
template <class Head, class... Tail> void dump_func(Head &&h, Tail &&...t) {
  cerr << h << (sizeof...(Tail) == 0 ? "" : ", "),
      dump_func(forward<Tail>(t)...);
}

struct Fast {
  Fast() {
    cin.tie(0);
    ios::sync_with_stdio(false);
  }
} fast;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
constexpr int MOD = 1000000007;
// *************** TEMPLATE END ***************

template <class T> T pow(T x, int n, const T UNION = 1) {
  T ret = UNION;
  while (n) {
    if (n & 1)
      ret *= x;
    x *= x;
    n >>= 1;
  }
  return ret;
}

template <int MD> struct ModInt {
  int x;
  static unordered_map<int, int> to_inv;
  ModInt() : x(0) {}
  ModInt(int x_) {
    if ((x = x_ % MD + MD) >= MD)
      x -= MD;
  }

  ModInt &operator+=(ModInt that) {
    if ((x += that.x) >= MD)
      x -= MD;
    return *this;
  }
  ModInt &operator*=(ModInt that) {
    x = (unsigned long long)x * that.x % MD;
    return *this;
  }
  ModInt &operator-=(ModInt that) {
    if ((x -= that.x) < 0)
      x += MD;
    return *this;
  }
  ModInt &operator/=(ModInt that) {
    x = (unsigned long long)x * that.inv().x % MD;
    return *this;
  }

  ModInt operator-() const { return -x < 0 ? MD - x : -x; }
  ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
  ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
  ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
  ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }
  bool operator==(ModInt that) const { return x == that.x; }
  bool operator!=(ModInt that) const { return x != that.x; }
  ModInt inv() const {
    return to_inv.count(this->x) ? to_inv[this->x]
                                 : (to_inv[this->x] = pow(*this, MD - 2).x);
  }
  friend ostream &operator<<(ostream &s, ModInt<MD> a) {
    s << a.x;
    return s;
  }
  friend istream &operator>>(istream &s, ModInt<MD> &a) {
    s >> a.x;
    return s;
  }
};
template <int MD> unordered_map<int, int> ModInt<MD>::to_inv;
using mint = ModInt<MOD>;

vector<mint> fact, fact_inv;
void init_factorial(int n) {
  fact = vector<mint>(n + 1, 1);
  fact_inv = vector<mint>(n + 1);
  for (int i = 0; i < n; i++)
    fact[i + 1] = fact[i] * (i + 1);
  fact_inv[n] = mint(1) / fact[n];
  for (int i = n - 1; i >= 0; i--)
    fact_inv[i] = fact_inv[i + 1] * (i + 1);
  // for (int i = 0; i < n + 1; i++) assert(fact[i] * fact_inv[i] == 1);
}
mint comb(int n, int r) { return fact[n] * fact_inv[r] * fact_inv[n - r]; }

// T0: 元の配列のモノイド
// T1: T0に対する作用素モノイド
template <class T0, class T1> class SegmentTree {
  // k番目のノードにのlazyを伝搬
  void eval(int k, int len) {
    // u1が正確に単位元ならいらない
    // if (lazy[k] == u1) return;
    // len個分のlazy[k]を評価
    node[k] = g(node[k], p(lazy[k], len));
    if (k < N - 1) {
      // 最下段でなければ下のlazyに伝搬
      lazy[2 * k + 1] = f1(lazy[2 * k + 1], lazy[k]);
      lazy[2 * k + 2] = f1(lazy[2 * k + 2], lazy[k]);
    }
    lazy[k] = u1;
  }
  // k番目のノード[l, r)について、[a, b)の範囲内にxを作用
  void update(int a, int b, T1 x, int k, int l, int r) {
    eval(k, r - l);
    if (b <= l || r <= a)
      return;
    if (a <= l && r <= b) {
      lazy[k] = f1(lazy[k], x);
      eval(k, r - l);
    } else {
      update(a, b, x, 2 * k + 1, l, (l + r) / 2);
      update(a, b, x, 2 * k + 2, (l + r) / 2, r);
      node[k] = f0(node[2 * k + 1], node[2 * k + 2]);
    }
  }
  // k番目のノード[l, r)について、[a, b)のクエリを求める
  T0 query(int a, int b, int k, int l, int r) {
    if (r <= a || b <= l)
      return u0;
    eval(k, r - l);
    if (a <= l && r <= b)
      return node[k];
    T0 vl = query(a, b, 2 * k + 1, l, (l + r) / 2);
    T0 vr = query(a, b, 2 * k + 2, (l + r) / 2, r);
    return f0(vl, vr);
  }

public:
  int sz; // 元の配列のサイズ
  int N;
  vector<T0> node;
  vector<T1> lazy;
  // T0上の演算、単位元
  using F0 = function<T0(T0, T0)>;
  F0 f0;
  T0 u0;
  // T1上の演算、単位元
  using F1 = function<T1(T1, T1)>;
  F1 f1;
  T1 u1;
  // 作用
  using G = function<T0(T0, T1)>;
  G g;
  // 多数のt1(T1)に対するf1の合成
  using P = function<T1(T1, int)>;
  P p;
  SegmentTree(const vector<T0> &a, F0 f0, T0 u0, F1 f1, T1 u1, G g, P p)
      : sz(a.size()), f0(f0), u0(u0), f1(f1), u1(u1), g(g), p(p) {
    for (N = 1; N < sz; N *= 2)
      ;
    node.resize(2 * N - 1);
    lazy.resize(2 * N - 1, u1);
    REP(i, sz) node[N - 1 + i] = a[i];
    for (int i = N - 2; i >= 0; i--)
      node[i] = f0(node[2 * i + 1], node[2 * i + 2]);
  }
  // [a, b)にxを作用
  void update(int a, int b, T1 x) {
    assert(0 <= a && a < b && b <= sz);
    update(a, b, x, 0, 0, N);
  }
  void update(int a, T1 x) { update(a, a + 1, x); }
  // [a, b)
  T0 query(int a, int b) { return query(a, b, 0, 0, N); }
  T0 query(int a) { return query(a, a + 1); }
};

signed main() {
  int n, H, D;
  cin >> n >> H >> D;
  init_factorial(n + 10);
  mint mul = 0;
  REPI(i, 1, n + 1) { mul += fact[i]; }

  vector<mint> dp(H + 1);
  dp[0] = fact[n] / mul;
  mint acc = dp[0];
  REPI(i, 1, H + 1) {
    dp[i] = acc * mul;
    acc += dp[i];
    if (i - D >= 0)
      acc -= dp[i - D];
  }
  cout << dp[H] << endl;
  ;
}