Problem p02625 (C++) — buggy submission, verdict: Time Limit Exceeded

/* #region Head */

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d)                                                       \\
  for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d)                                                      \\
  for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                \\
  sort(ALL(c));                                                                \\
  for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());

#define endl '\\n'
#define sqrt sqrtl
#define floor floorl
#define log2 log2l

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T>
istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
  for (T &x : vec)
    is >> x;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, vc<T> &vec) { // vector 出力 (for dump)
  os << "{";
  REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
  os << "}";
  return os;
}
template <typename T>
ostream &operator>>(ostream &os, vc<T> &vec) { // vector 出力 (inline)
  REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\\n" : " ");
  return os;
}

template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
  is >> pair_var.first >> pair_var.second;
  return is;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) { // pair 出力
  os << "(" << pair_var.first << ", " << pair_var.second << ")";
  return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, T &map_var) {
  os << "{";
  REPI(itr, map_var) {
    os << *itr;
    auto itrcp = itr;
    if (++itrcp != map_var.end())
      os << ", ";
  }
  return os << "}";
}
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
  return out_iter(os, map_var);
}
template <typename T, typename U>
ostream &operator<<(ostream &os, um<T, U> &map_var) {
  os << "{";
  REPI(itr, map_var) {
    auto [key, value] = *itr;
    os << "(" << key << ", " << value << ")";
    auto itrcp = itr;
    if (++itrcp != map_var.end())
      os << ", ";
  }
  os << "}";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) {
  return out_iter(os, set_var);
}
template <typename T> ostream &operator<<(ostream &os, us<T> &set_var) {
  return out_iter(os, set_var);
}
template <typename T> ostream &operator<<(ostream &os, pq<T> &pq_var) {
  pq<T> pq_cp(pq_var);
  os << "{";
  if (!pq_cp.empty()) {
    os << pq_cp.top(), pq_cp.pop();
    while (!pq_cp.empty())
      os << ", " << pq_cp.top(), pq_cp.pop();
  }
  return os << "}";
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&...tail) {
  DUMPOUT << head;
  if (sizeof...(Tail) > 0)
    DUMPOUT << ", ";
  dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmax(T &xmax, const U &x, Comp comp = {}) {
  if (comp(xmax, x)) {
    xmax = x;
    return true;
  }
  return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmin(T &xmin, const U &x, Comp comp = {}) {
  if (comp(x, xmin)) {
    xmin = x;
    return true;
  }
  return false;
}

// ローカル用
#define DEBUG_

#ifdef DEBUG_
#define DEB
#define dump(...)                                                              \\
  DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                              \\
          << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl  \\
          << "    ",                                                           \\
      dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

struct AtCoderInitialize {
  static constexpr int IOS_PREC = 15;
  static constexpr bool AUTOFLUSH = false;
  AtCoderInitialize() {
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    cout << fixed << setprecision(IOS_PREC);
    if (AUTOFLUSH)
      cout << unitbuf;
  }
} ATCODER_INITIALIZE;

void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }

/* #endregion */

/* #region mint */

// 自動で MOD を取る整数
struct mint {
  ll x;
  mint(ll x = 0) : x((x % MOD + MOD) % MOD) {}
  mint &operator+=(const mint a) {
    if ((x += a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += MOD - a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  // O(log(t))
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1); // ⌊t/2⌋ 乗
    a *= a;               // ⌊t/2⌋*2 乗
    if (t & 1)            // ⌊t/2⌋*2 == t-1 のとき
      a *= *this;         // ⌊t/2⌋*2+1 乗 => t 乗
    return a;
  }

  // for prime mod
  mint inv() const {
    return pow(MOD - 2); // オイラーの定理から， x^(-1) ≡ x^(p-2)
  }
  mint &operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
  bool operator==(const mint a) const { return this->x == a.x; }
  bool operator==(const ll a) const { return this->x == a; }

  // mint 入力
  friend istream &operator>>(istream &is, mint &x) {
    is >> x.x;
    return is;
  }

  // mint 出力
  friend ostream &operator<<(ostream &os, mint x) {
    os << x.x;
    return os;
  }
};

/* #endregion */

/* #region Comb1 */

// 二項係数計算用クラス．1 <= k <= n <= 1e7 程度用．
class Combinaion {
private:
  /* テーブルの大きさの既定値．(MAX)! まで計算できる． */
  static constexpr ll MAX = 1e6 + 11;
  /* 実際のテーブルの大きさ． */
  ll max;
  /* 階乗を格納するテーブル．fac[n] := n! % MOD. */
  vc<mint> fac;
  /* 階乗の逆元を格納するテーブル．finv[n] := (fac[n])^(-1). */
  vc<mint> finv;

  /* 各種テーブルを初期化する． */
  void init(int n) {
    max = n;
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    REPM(i, 2, n) fac[i] = fac[i - 1] * i;
    finv[n] = fac[n].inv();
    REPR(i, n, 2) finv[i - 1] = finv[i] * i;
  }

public:
  /* コンストラクタ． */
  Combinaion(int n = MAX) : fac(n + 1), finv(n + 1) { init(n); }

  /* 二項係数 nCk % MOD を計算する． */
  mint operator()(ll n, ll k) const {
    assert(n <= max); // ここで詰まると RE
    assert(k <= max);
    if (n < k || n < 0 || k < 0)
      return 0;
    return fac[n] * finv[k] * finv[n - k];
  }

  mint perm(ll n, ll k) { return fac[n] * finv[n - k]; }

  // 重複組み合わせ nHr % MOD を計算する
  mint homogeneous(ll n, ll r) { return (*this)(n + r - 1, r); }
};

/* #endregion */

// Problem
void solve() {
  ll n, m;
  cin >> n >> m;

  mint ret = 0;
  Combinaion c;
  REPM(i, 0, n) {
    mint d = c(n, i) * c.perm(m, i) * c.perm(m - i, n - i).pow(2);
    if (i % 2 == 0)
      ret += d;
    else
      ret -= d;
  }
  cout << ret << endl;
}

// entry point
int main() {
  solve();
  return 0;
}


Error: TLE

Fixed submission:

/* #region Head */

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d)                                                       \\
  for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d)                                                      \\
  for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                \\
  sort(ALL(c));                                                                \\
  for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());

#define endl '\\n'
#define sqrt sqrtl
#define floor floorl
#define log2 log2l

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T>
istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
  for (T &x : vec)
    is >> x;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, vc<T> &vec) { // vector 出力 (for dump)
  os << "{";
  REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
  os << "}";
  return os;
}
template <typename T>
ostream &operator>>(ostream &os, vc<T> &vec) { // vector 出力 (inline)
  REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\\n" : " ");
  return os;
}

template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
  is >> pair_var.first >> pair_var.second;
  return is;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) { // pair 出力
  os << "(" << pair_var.first << ", " << pair_var.second << ")";
  return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, T &map_var) {
  os << "{";
  REPI(itr, map_var) {
    os << *itr;
    auto itrcp = itr;
    if (++itrcp != map_var.end())
      os << ", ";
  }
  return os << "}";
}
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
  return out_iter(os, map_var);
}
template <typename T, typename U>
ostream &operator<<(ostream &os, um<T, U> &map_var) {
  os << "{";
  REPI(itr, map_var) {
    auto [key, value] = *itr;
    os << "(" << key << ", " << value << ")";
    auto itrcp = itr;
    if (++itrcp != map_var.end())
      os << ", ";
  }
  os << "}";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) {
  return out_iter(os, set_var);
}
template <typename T> ostream &operator<<(ostream &os, us<T> &set_var) {
  return out_iter(os, set_var);
}
template <typename T> ostream &operator<<(ostream &os, pq<T> &pq_var) {
  pq<T> pq_cp(pq_var);
  os << "{";
  if (!pq_cp.empty()) {
    os << pq_cp.top(), pq_cp.pop();
    while (!pq_cp.empty())
      os << ", " << pq_cp.top(), pq_cp.pop();
  }
  return os << "}";
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&...tail) {
  DUMPOUT << head;
  if (sizeof...(Tail) > 0)
    DUMPOUT << ", ";
  dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmax(T &xmax, const U &x, Comp comp = {}) {
  if (comp(xmax, x)) {
    xmax = x;
    return true;
  }
  return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmin(T &xmin, const U &x, Comp comp = {}) {
  if (comp(x, xmin)) {
    xmin = x;
    return true;
  }
  return false;
}

// ローカル用
#define DEBUG_

#ifdef DEBUG_
#define DEB
#define dump(...)                                                              \\
  DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                              \\
          << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl  \\
          << "    ",                                                           \\
      dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

struct AtCoderInitialize {
  static constexpr int IOS_PREC = 15;
  static constexpr bool AUTOFLUSH = false;
  AtCoderInitialize() {
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    cout << fixed << setprecision(IOS_PREC);
    if (AUTOFLUSH)
      cout << unitbuf;
  }
} ATCODER_INITIALIZE;

void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }

/* #endregion */

/* #region mint */

// 自動で MOD を取る整数
struct mint {
  ll x;
  mint(ll x = 0) : x((x % MOD + MOD) % MOD) {}
  mint &operator+=(const mint a) {
    if ((x += a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += MOD - a.x) >= MOD)
      x -= MOD;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  // O(log(t))
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1); // ⌊t/2⌋ 乗
    a *= a;               // ⌊t/2⌋*2 乗
    if (t & 1)            // ⌊t/2⌋*2 == t-1 のとき
      a *= *this;         // ⌊t/2⌋*2+1 乗 => t 乗
    return a;
  }

  // for prime mod
  mint inv() const {
    return pow(MOD - 2); // オイラーの定理から， x^(-1) ≡ x^(p-2)
  }
  mint &operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
  bool operator==(const mint a) const { return this->x == a.x; }
  bool operator==(const ll a) const { return this->x == a; }

  // mint 入力
  friend istream &operator>>(istream &is, mint &x) {
    is >> x.x;
    return is;
  }

  // mint 出力
  friend ostream &operator<<(ostream &os, mint x) {
    os << x.x;
    return os;
  }
};

/* #endregion */

// Problem
void solve() {
  ll n, m;
  cin >> n >> m;

  // ナイーブな実装
  vc<vc<mint>> dp(2, vc<mint>(m + 1, 0));
  dp[0][m - n] = 1; // TODO
  // mint d = m - n;
  REP(i, 0, n) {
    // 配る
    REPM(j, m - n, m) dp[(i + 1) % 2][j] = 0;
    REPM(j, m - n, m) {
      dp[(i + 1) % 2][j] += dp[i % 2][j] * j;
      if (j + 1 <= m)
        dp[(i + 1) % 2][j + 1] += dp[i % 2][j] * (n - i - 1);
    }
    dump(i, dp[(i + 1) % 2]);
  }
  // dump(dp);
  mint ret = accumulate(ALL(dp[n % 2]), mint(0));
  // ret *= mint(m).pow(n); // mPn
  REP(i, 0, n) ret *= m - i;
  cout << ret << endl;
}

// entry point
int main() {
  solve();
  return 0;
}