Problem p03082 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <algorithm>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstdio>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>

#define MOD 1000000007
#define MOD2 998244353
#define int long long
// #define PI 3.14159265358979

#define rep(i, n) for (int i = 0; i < (int)(n); i++)

using namespace std;

template <typename T> ostream &operator<<(ostream &os, const vector<T> &A) {
  for (int i = 0; i < A.size(); i++)
    os << A[i] << " ";
  os << endl;
  return os;
}
template <> ostream &operator<<(ostream &os, const vector<vector<int>> &A) {
  int N = A.size();
  int M;
  if (N > 0)
    M = A[0].size();
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < M; j++)
      os << A[i][j] << " ";
    os << endl;
  }
  return os;
}

typedef pair<int, int> pii;
typedef long long ll;

struct edge {
  int from, to, d, c;
  edge(int _from = 0, int _to = 0, int _d = 0, int _c = 0) {
    from = _from;
    to = _to;
    d = _d;
    c = _c;
  }
  bool operator<(const edge &rhs) const {
    return (d == rhs.d) ? (c < rhs.c) : (d < rhs.d);
  }
};
struct aabb {
  int x1, y1, x2, y2;
  aabb(int x1, int y1, int x2, int y2) : x1(x1), y1(y1), x2(x2), y2(y2) {}
};

typedef vector<edge> edges;
typedef vector<edges> graph;
struct flow {
  int to, cap, rev, cost;
  flow(int to = 0, int cap = 0, int rev = 0, int cost = 0)
      : to(to), cap(cap), rev(rev), cost(cost) {}
};
typedef vector<vector<flow>> flows;

const int di[4] = {0, -1, 0, 1};
const int dj[4] = {-1, 0, 1, 0};
const int ci[5] = {0, 0, -1, 0, 1};
const int cj[5] = {0, -1, 0, 1, 0};
const ll LINF = LLONG_MAX / 2;
const int INF = INT_MAX / 2;
const double PI = acos(-1);

int pow2(int n) { return 1 << n; }
template <typename T, typename U> bool chmin(T &x, const U &y) {
  if (x > y) {
    x = y;
    return true;
  }
  return false;
}
template <typename T, typename U> bool chmax(T &x, const U &y) {
  if (x < y) {
    x = y;
    return true;
  }
  return false;
}

struct initializer {
  initializer() { cout << fixed << setprecision(20); }
};
initializer _____;
ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
ll extgcd(ll a, ll b, ll &x, ll &y) {
  int d = a;
  if (b != 0) {
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  } else {
    x = 1;
    y = 0;
  }
  return d;
}
ll factorial(ll x) {
  if (x == 1)
    return 1;
  else
    return x * factorial(x - 1);
}
ll Mfactorial(ll x, ll m) {
  ll ret = 1;
  for (ll i = 1; i <= x; i++) {
    ret *= i;
    ret %= m;
  }
  return ret;
}
vector<int> MfactTable(int n, int m) {
  vector<int> ret(n + 1);
  ret[0] = 1;
  int tmp = 1;
  for (int i = 1; i <= n; i++) {
    tmp *= i;
    tmp %= m;
    ret[i] = tmp;
  }
  return ret;
}
int Minverse(int a, int m) {
  int x, y;
  extgcd(a, m, x, y);
  return (m + x % m) % m;
}
int McombSmall(int n, int k, int m) {
  // O(n)
  int ret = Mfactorial(n, m);
  ret *= Minverse(Mfactorial(k, m), m);
  ret %= m;
  ret *= Minverse(Mfactorial(n - k, m), m);
  return ret % m;
}
int McombFromFactTable(vector<int> &T, int n, int k, int m) {
  if (k > n)
    return 0;
  int ret = T[n];
  ret *= Minverse(T[k], m);
  ret %= m;
  ret *= Minverse(T[n - k], m);
  return ret % m;
}
ll pow(ll x, int n) {
  if (n == 0)
    return 1;
  ll ret = (n & 1) ? x : 1;
  ll a = pow(x, n / 2);
  return ret * a * a;
}
ll Mpow(ll x, int n, int m) {
  if (n == 0)
    return 1;
  ll ret = (n & 1) ? x : 1;
  ll a = Mpow(x, n / 2, m);
  return (((ret * a) % m) * a) % m;
}
vector<vector<int>> combTable(int N) {
  vector<vector<int>> ret(N + 1, vector<int>(N + 1));
  for (int i = 0; i <= N; i++)
    for (int j = 0; j <= i; j++) {
      if (j == 0 || j == i)
        ret[i][j] = 1;
      else
        ret[i][j] = ret[i - 1][j - 1] + ret[i - 1][j];
    }
  return ret;
}
int countNmodPisQlr(int l, int r, int P, int Q) {
  // r>=l>=0
  return (r - Q + P) / P - (l - Q + P - 1) / P;
}
int N, M, K, T, Q, H, W;
signed main() {
  cin >> N >> K;
  vector<int> A(N);
  rep(i, N) cin >> A[i];
  sort(A.rbegin(), A.rend());
  vector<int> t = MfactTable(N, MOD);
  vector<vector<int>> dp(N + 1, vector<int>(1e5 + 10, 0));
  dp[0][K] = 1;
  rep(i, N) rep(j, dp[0].size()) {
    dp[i + 1][j] = (dp[i + 1][j] +
                    dp[i][j] * (N - i - 1) % MOD * Minverse(N - i, MOD) % MOD) %
                   MOD;
    dp[i + 1][j % A[i]] =
        (dp[i + 1][j % A[i]] + dp[i][j] * Minverse(N - i, MOD) % MOD) % MOD;
  }
  int ans = 0;
  rep(j, A[N - 1]) { ans = (ans + dp[N][j] * j % MOD) % MOD; }
  ans = ans * t[N] % MOD;
  cout << ans << endl;
  return 0;
}

Fixed submission:
#include <algorithm>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstdio>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>

#define MOD 1000000007
#define MOD2 998244353
#define int long long
// #define PI 3.14159265358979

#define rep(i, n) for (int i = 0; i < (int)(n); i++)

using namespace std;

template <typename T> ostream &operator<<(ostream &os, const vector<T> &A) {
  for (int i = 0; i < A.size(); i++)
    os << A[i] << " ";
  os << endl;
  return os;
}
template <> ostream &operator<<(ostream &os, const vector<vector<int>> &A) {
  int N = A.size();
  int M;
  if (N > 0)
    M = A[0].size();
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < M; j++)
      os << A[i][j] << " ";
    os << endl;
  }
  return os;
}

typedef pair<int, int> pii;
typedef long long ll;

struct edge {
  int from, to, d, c;
  edge(int _from = 0, int _to = 0, int _d = 0, int _c = 0) {
    from = _from;
    to = _to;
    d = _d;
    c = _c;
  }
  bool operator<(const edge &rhs) const {
    return (d == rhs.d) ? (c < rhs.c) : (d < rhs.d);
  }
};
struct aabb {
  int x1, y1, x2, y2;
  aabb(int x1, int y1, int x2, int y2) : x1(x1), y1(y1), x2(x2), y2(y2) {}
};

typedef vector<edge> edges;
typedef vector<edges> graph;
struct flow {
  int to, cap, rev, cost;
  flow(int to = 0, int cap = 0, int rev = 0, int cost = 0)
      : to(to), cap(cap), rev(rev), cost(cost) {}
};
typedef vector<vector<flow>> flows;

const int di[4] = {0, -1, 0, 1};
const int dj[4] = {-1, 0, 1, 0};
const int ci[5] = {0, 0, -1, 0, 1};
const int cj[5] = {0, -1, 0, 1, 0};
const ll LINF = LLONG_MAX / 2;
const int INF = INT_MAX / 2;
const double PI = acos(-1);

int pow2(int n) { return 1 << n; }
template <typename T, typename U> bool chmin(T &x, const U &y) {
  if (x > y) {
    x = y;
    return true;
  }
  return false;
}
template <typename T, typename U> bool chmax(T &x, const U &y) {
  if (x < y) {
    x = y;
    return true;
  }
  return false;
}

struct initializer {
  initializer() { cout << fixed << setprecision(20); }
};
initializer _____;
ll gcd(ll a, ll b) {
  if (b == 0)
    return a;
  else
    return gcd(b, a % b);
}
ll extgcd(ll a, ll b, ll &x, ll &y) {
  int d = a;
  if (b != 0) {
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  } else {
    x = 1;
    y = 0;
  }
  return d;
}
ll factorial(ll x) {
  if (x == 1)
    return 1;
  else
    return x * factorial(x - 1);
}
ll Mfactorial(ll x, ll m) {
  ll ret = 1;
  for (ll i = 1; i <= x; i++) {
    ret *= i;
    ret %= m;
  }
  return ret;
}
vector<int> MfactTable(int n, int m) {
  vector<int> ret(n + 1);
  ret[0] = 1;
  int tmp = 1;
  for (int i = 1; i <= n; i++) {
    tmp *= i;
    tmp %= m;
    ret[i] = tmp;
  }
  return ret;
}
int Minverse(int a, int m) {
  int x, y;
  extgcd(a, m, x, y);
  return (m + x % m) % m;
}
int McombSmall(int n, int k, int m) {
  // O(n)
  int ret = Mfactorial(n, m);
  ret *= Minverse(Mfactorial(k, m), m);
  ret %= m;
  ret *= Minverse(Mfactorial(n - k, m), m);
  return ret % m;
}
int McombFromFactTable(vector<int> &T, int n, int k, int m) {
  if (k > n)
    return 0;
  int ret = T[n];
  ret *= Minverse(T[k], m);
  ret %= m;
  ret *= Minverse(T[n - k], m);
  return ret % m;
}
ll pow(ll x, int n) {
  if (n == 0)
    return 1;
  ll ret = (n & 1) ? x : 1;
  ll a = pow(x, n / 2);
  return ret * a * a;
}
ll Mpow(ll x, int n, int m) {
  if (n == 0)
    return 1;
  ll ret = (n & 1) ? x : 1;
  ll a = Mpow(x, n / 2, m);
  return (((ret * a) % m) * a) % m;
}
vector<vector<int>> combTable(int N) {
  vector<vector<int>> ret(N + 1, vector<int>(N + 1));
  for (int i = 0; i <= N; i++)
    for (int j = 0; j <= i; j++) {
      if (j == 0 || j == i)
        ret[i][j] = 1;
      else
        ret[i][j] = ret[i - 1][j - 1] + ret[i - 1][j];
    }
  return ret;
}
int countNmodPisQlr(int l, int r, int P, int Q) {
  // r>=l>=0
  return (r - Q + P) / P - (l - Q + P - 1) / P;
}
int N, M, K, T, Q, H, W;
signed main() {
  cin >> N >> K;
  vector<int> A(N);
  rep(i, N) cin >> A[i];
  sort(A.rbegin(), A.rend());
  vector<int> t = MfactTable(N, MOD);
  vector<vector<int>> dp(N + 1, vector<int>(1e5 + 10, 0));
  dp[0][K] = 1;
  rep(i, N) {
    int div = Minverse(N - i, MOD);
    rep(j, dp[0].size()) {
      dp[i + 1][j] =
          (dp[i + 1][j] + dp[i][j] * (N - i - 1) % MOD * div % MOD) % MOD;
      dp[i + 1][j % A[i]] = (dp[i + 1][j % A[i]] + dp[i][j] * div % MOD) % MOD;
    }
  }
  int ans = 0;
  rep(j, A[N - 1]) { ans = (ans + dp[N][j] * j % MOD) % MOD; }
  ans = ans * t[N] % MOD;
  cout << ans << endl;
  return 0;
}