Problem p02810 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;
/*#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<typename T> using gpp_set = tree<T, null_type, less<T>, rb_tree_tag,
tree_order_statistics_node_update>; template<typename T, typename L> using
gpp_map = tree<T, L, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using gpp_multiset = tree<T, null_type, less_equal<T>,
rb_tree_tag, tree_order_statistics_node_update>;*/
struct fast_ios {
  fast_ios() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
#define FOR(i, begin, end) for (int i = (begin); i < (end); i++)
#define REP(i, n) FOR(i, 0, n)
#define IFOR(i, begin, end) for (int i = (end)-1; i >= (begin); i--)
#define IREP(i, n) IFOR(i, 0, n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(), v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x)                                                      \
  distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x)                                                      \
  distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL << (n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v)                                                              \
  {                                                                            \
    cout << #v << "=" << endl;                                                 \
    REP(i_debug, v.size()) { cout << v[i_debug] << ","; }                      \
    cout << endl;                                                              \
  }
#define mdebug(m)                                                              \
  {                                                                            \
    cout << #m << "=" << endl;                                                 \
    REP(i_debug, m.size()) {                                                   \
      REP(j_debug, m[i_debug].size()) { cout << m[i_debug][j_debug] << ","; }  \
      cout << endl;                                                            \
    }                                                                          \
  }
#define Return(ans)                                                            \
  {                                                                            \
    cout << (ans) << endl;                                                     \
    return 0;                                                                  \
  }
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (int i = 0; i < v.size(); i++) {
    cout << v[i];
    if (i != v.size() - 1)
      cout << endl;
  };
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> p) {
  cout << '(' << p.first << ',' << p.second << ')';
  return os;
}
template <typename T> void Out(T x) { cout << x << endl; }
template <typename T1, typename T2> void Ans(bool f, T1 y, T2 n) {
  if (f)
    Out(y);
  else
    Out(n);
}

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

// int dx[4] = {1,0,-1,0};
// int dy[4] = {0,1,0,-1};
// char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
// const int mod = 998244353;
// #define Add(x, y) x = (x + (y)) % mod
// #define Mult(x, y) x = (x * (y)) % mod

template <long long MOD> struct ModInt {

  using ll = long long;
  ll val;

  void setval(ll v) { val = v % MOD; };
  ModInt() : val(0) {}
  ModInt(ll v) { setval(v); };

  ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); }
  ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); }
  ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); }
  ModInt operator/(const ModInt &x) const { return *this * x.inv(); }
  ModInt operator-() const { return ModInt(MOD - val); }
  ModInt operator+=(const ModInt &x) { return *this = *this + x; }
  ModInt operator-=(const ModInt &x) { return *this = *this - x; }
  ModInt operator*=(const ModInt &x) { return *this = *this * x; }
  ModInt operator/=(const ModInt &x) { return *this = *this / x; }

  friend ostream &operator<<(ostream &os, const ModInt &x) {
    os << x.val;
    return os;
  }
  friend istream &operator>>(istream &is, ModInt &x) {
    is >> x.val;
    x.val = (x.val % MOD + MOD) % MOD;
    return is;
  }

  ModInt pow(ll n) const {
    ModInt a = 1;
    if (n == 0)
      return a;
    int i0 = 64 - __builtin_clzll(n);
    for (int i = i0 - 1; i >= 0; i--) {
      a = a * a;
      if ((n >> i) & 1)
        a *= (*this);
    }
    return a;
  }
  ModInt inv() const { return this->pow(MOD - 2); }
};

using mint = ModInt<mod>;
mint pow(mint x, long long n) { return x.pow(n); }
// using mint = double; //for debug
using mvec = vector<mint>;
using mmat = vector<mvec>;

struct Combination {

  vector<mint> fact, invfact;

  Combination(int N) {
    fact = vector<mint>({mint(1)});
    invfact = vector<mint>({mint(1)});
    fact_initialize(N);
  }

  void fact_initialize(int N) {
    int i0 = fact.size();
    if (i0 >= N + 1)
      return;
    fact.resize(N + 1);
    invfact.resize(N + 1);
    for (int i = i0; i <= N; i++)
      fact[i] = fact[i - 1] * i;
    invfact[N] = (mint)1 / fact[N];
    for (int i = N - 1; i >= i0; i--)
      invfact[i] = invfact[i + 1] * (i + 1);
  }

  mint nCr(int n, int r) {
    if (n < 0 || r < 0 || r > n)
      return mint(0);
    if (fact.size() < n + 1)
      fact_initialize(n);
    return fact[n] * invfact[r] * invfact[n - r];
  }

  mint nPr(int n, int r) {
    if (n < 0 || r < 0 || r > n)
      return mint(0);
    if (fact.size() < n + 1)
      fact_initialize(n);
    return fact[n] * invfact[n - r];
  }
};

mint dp[100][100][501] = {};

signed main() {

  int N, X;
  cin >> N >> X;
  vec L(N);
  cin >> L;

  Sort(L);
  Reverse(L);

  dp[0][0][L[0]] = 1;
  FOR(i, 1, N) {
    int jmax = max(i, X / L[i - 1]);
    REP(j, jmax) FOR(k, L[0], X + 1) {
      int t = k - L[i] + 1 - j * (L[i] - 1);
      if (t > 0)
        dp[i][j][k] += dp[i - 1][j][k] * t;

      if (k + L[i] <= X)
        dp[i][j + 1][k + L[i]] += dp[i - 1][j][k] * (2 + j);

      FOR(l, 1, L[i]) if (k + l <= X) {
        dp[i][j][k + l] += dp[i - 1][j][k] * 2 * (j + 1);
      }

      if (j > 0) {
        FOR(l, 0, L[i] - 1) if (k + l <= X) {
          dp[i][j - 1][k + l] += dp[i - 1][j][k] * j * (L[i] - 1 - l);
        }
      }
    }
  }

  mint ans = 0;
  REP(j, N) ans += dp[N - 1][j][X];
  Out(ans);

  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
/*#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<typename T> using gpp_set = tree<T, null_type, less<T>, rb_tree_tag,
tree_order_statistics_node_update>; template<typename T, typename L> using
gpp_map = tree<T, L, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using gpp_multiset = tree<T, null_type, less_equal<T>,
rb_tree_tag, tree_order_statistics_node_update>;*/
struct fast_ios {
  fast_ios() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
#define FOR(i, begin, end) for (int i = (begin); i < (end); i++)
#define REP(i, n) FOR(i, 0, n)
#define IFOR(i, begin, end) for (int i = (end)-1; i >= (begin); i--)
#define IREP(i, n) IFOR(i, 0, n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(), v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x)                                                      \
  distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x)                                                      \
  distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL << (n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v)                                                              \
  {                                                                            \
    cout << #v << "=" << endl;                                                 \
    REP(i_debug, v.size()) { cout << v[i_debug] << ","; }                      \
    cout << endl;                                                              \
  }
#define mdebug(m)                                                              \
  {                                                                            \
    cout << #m << "=" << endl;                                                 \
    REP(i_debug, m.size()) {                                                   \
      REP(j_debug, m[i_debug].size()) { cout << m[i_debug][j_debug] << ","; }  \
      cout << endl;                                                            \
    }                                                                          \
  }
#define Return(ans)                                                            \
  {                                                                            \
    cout << (ans) << endl;                                                     \
    return 0;                                                                  \
  }
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template <typename T> istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v)
    is >> x;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, vector<T> &v) {
  for (int i = 0; i < v.size(); i++) {
    cout << v[i];
    if (i != v.size() - 1)
      cout << endl;
  };
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> p) {
  cout << '(' << p.first << ',' << p.second << ')';
  return os;
}
template <typename T> void Out(T x) { cout << x << endl; }
template <typename T1, typename T2> void Ans(bool f, T1 y, T2 n) {
  if (f)
    Out(y);
  else
    Out(n);
}

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

// int dx[4] = {1,0,-1,0};
// int dy[4] = {0,1,0,-1};
// char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
// const int mod = 998244353;
// #define Add(x, y) x = (x + (y)) % mod
// #define Mult(x, y) x = (x * (y)) % mod

template <long long MOD> struct ModInt {

  using ll = long long;
  ll val;

  void setval(ll v) { val = v % MOD; };
  ModInt() : val(0) {}
  ModInt(ll v) { setval(v); };

  ModInt operator+(const ModInt &x) const { return ModInt(val + x.val); }
  ModInt operator-(const ModInt &x) const { return ModInt(val - x.val + MOD); }
  ModInt operator*(const ModInt &x) const { return ModInt(val * x.val); }
  ModInt operator/(const ModInt &x) const { return *this * x.inv(); }
  ModInt operator-() const { return ModInt(MOD - val); }
  ModInt operator+=(const ModInt &x) { return *this = *this + x; }
  ModInt operator-=(const ModInt &x) { return *this = *this - x; }
  ModInt operator*=(const ModInt &x) { return *this = *this * x; }
  ModInt operator/=(const ModInt &x) { return *this = *this / x; }

  friend ostream &operator<<(ostream &os, const ModInt &x) {
    os << x.val;
    return os;
  }
  friend istream &operator>>(istream &is, ModInt &x) {
    is >> x.val;
    x.val = (x.val % MOD + MOD) % MOD;
    return is;
  }

  ModInt pow(ll n) const {
    ModInt a = 1;
    if (n == 0)
      return a;
    int i0 = 64 - __builtin_clzll(n);
    for (int i = i0 - 1; i >= 0; i--) {
      a = a * a;
      if ((n >> i) & 1)
        a *= (*this);
    }
    return a;
  }
  ModInt inv() const { return this->pow(MOD - 2); }
};

using mint = ModInt<mod>;
mint pow(mint x, long long n) { return x.pow(n); }
// using mint = double; //for debug
using mvec = vector<mint>;
using mmat = vector<mvec>;

struct Combination {

  vector<mint> fact, invfact;

  Combination(int N) {
    fact = vector<mint>({mint(1)});
    invfact = vector<mint>({mint(1)});
    fact_initialize(N);
  }

  void fact_initialize(int N) {
    int i0 = fact.size();
    if (i0 >= N + 1)
      return;
    fact.resize(N + 1);
    invfact.resize(N + 1);
    for (int i = i0; i <= N; i++)
      fact[i] = fact[i - 1] * i;
    invfact[N] = (mint)1 / fact[N];
    for (int i = N - 1; i >= i0; i--)
      invfact[i] = invfact[i + 1] * (i + 1);
  }

  mint nCr(int n, int r) {
    if (n < 0 || r < 0 || r > n)
      return mint(0);
    if (fact.size() < n + 1)
      fact_initialize(n);
    return fact[n] * invfact[r] * invfact[n - r];
  }

  mint nPr(int n, int r) {
    if (n < 0 || r < 0 || r > n)
      return mint(0);
    if (fact.size() < n + 1)
      fact_initialize(n);
    return fact[n] * invfact[n - r];
  }
};

mint dp[100][100][501] = {};

signed main() {

  int N, X;
  cin >> N >> X;
  vec L(N);
  cin >> L;

  Sort(L);
  Reverse(L);

  dp[0][0][L[0]] = 1;
  FOR(i, 1, N) {
    int jmax = min(i, X / L[i - 1]);
    REP(j, jmax) FOR(k, L[0], X + 1) {
      int t = k - L[i] + 1 - j * (L[i] - 1);
      if (t > 0)
        dp[i][j][k] += dp[i - 1][j][k] * t;

      if (k + L[i] <= X)
        dp[i][j + 1][k + L[i]] += dp[i - 1][j][k] * (2 + j);

      FOR(l, 1, L[i]) if (k + l <= X) {
        dp[i][j][k + l] += dp[i - 1][j][k] * 2 * (j + 1);
      }

      if (j > 0) {
        FOR(l, 0, L[i] - 1) if (k + l <= X) {
          dp[i][j - 1][k + l] += dp[i - 1][j][k] * j * (L[i] - 1 - l);
        }
      }
    }
  }

  mint ans = 0;
  REP(j, N) ans += dp[N - 1][j][X];
  Out(ans);

  return 0;
}