Problem p02974 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll MOD = 1e9 + 7;

template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

template <uint_fast64_t Modulus> class modint {
  using u64 = uint_fast64_t;

public:
  u64 a;
  constexpr modint(const u64 x = 0) noexcept
      : a(((x % Modulus) + Modulus) % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint &operator+=(const modint &rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus)
      a -= Modulus;
    return *this;
  }
  constexpr modint operator+(const modint &rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint &operator++() noexcept { return ++a, *this; }
  constexpr modint operator++(int) noexcept {
    modint t = *this;
    return ++a, t;
  }
  constexpr modint &operator-=(const modint &rhs) noexcept {
    if (a < rhs.a)
      a += Modulus;
    a -= rhs.a;
    return *this;
  }
  constexpr modint operator-(const modint &rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint &operator--() noexcept { return --a, *this; }
  constexpr modint operator--(int) noexcept {
    modint t = *this;
    return --a, t;
  }
  constexpr modint &operator*=(const modint &rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint operator*(const modint &rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp & 1)
        *this *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return *this;
  }
  constexpr modint operator/(const modint &rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint operator-() const noexcept { return modint(Modulus - a); }
  constexpr bool operator==(const modint &rhs) const noexcept {
    return a == rhs.a;
  }
  constexpr bool operator!=(const modint &rhs) const noexcept {
    return a != rhs.a;
  }
  constexpr bool operator!() const noexcept { return !a; }
  friend constexpr modint pow(modint rhs, long long exp) noexcept {
    modint res{1};
    while (exp) {
      if (exp & 1)
        res *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return res;
  }
  template <class T> friend constexpr modint operator+(T x, modint y) noexcept {
    return modint(x) + y;
  }
  template <class T> friend constexpr modint operator-(T x, modint y) noexcept {
    return modint(x) - y;
  }
  template <class T> friend constexpr modint operator*(T x, modint y) noexcept {
    return modint(x) * y;
  }
  template <class T> friend constexpr modint operator/(T x, modint y) noexcept {
    return modint(x) / y;
  }
  friend ostream &operator<<(ostream &s, const modint &rhs) noexcept {
    return s << rhs.a;
  }
  friend istream &operator>>(istream &s, modint &rhs) noexcept {
    u64 a;
    rhs = modint{(s >> a, a)};
    return s;
  }
};

using mint = modint<MOD>;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N, K;
  cin >> N >> K;
  mint dp[N + 1][N + 1][K + 1];
  for (int i = 0; i < N + 1; ++i)
    for (int j = 0; j < N + 1; ++j)
      for (int k = 0; k < K + 1; ++k)
        dp[i][j][k] = 0;
  dp[0][0][0] = 1;
  for (int i = 0; i < N; ++i) {
    for (int j = 0; j < N + 1; ++j) {
      for (int k = 0; j + k < K + 1; ++k) {
        dp[i + 1][j][j + k] += dp[i][j][k] + dp[i][j][k] * j;
        if (1 < j)
          dp[i + 1][j - 2][j + k] += dp[i][j][k] * j * j / 4;
        if (j < K - 1)
          dp[i + 1][j + 2][j + k] += dp[i][j][k];
      }
    }
  }
  cout << dp[N][0][K] << endl;
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll MOD = 1e9 + 7;

template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

template <uint_fast64_t Modulus> class modint {
  using u64 = uint_fast64_t;

public:
  u64 a;
  constexpr modint(const u64 x = 0) noexcept
      : a(((x % Modulus) + Modulus) % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint &operator+=(const modint &rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus)
      a -= Modulus;
    return *this;
  }
  constexpr modint operator+(const modint &rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint &operator++() noexcept { return ++a, *this; }
  constexpr modint operator++(int) noexcept {
    modint t = *this;
    return ++a, t;
  }
  constexpr modint &operator-=(const modint &rhs) noexcept {
    if (a < rhs.a)
      a += Modulus;
    a -= rhs.a;
    return *this;
  }
  constexpr modint operator-(const modint &rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint &operator--() noexcept { return --a, *this; }
  constexpr modint operator--(int) noexcept {
    modint t = *this;
    return --a, t;
  }
  constexpr modint &operator*=(const modint &rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint operator*(const modint &rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp & 1)
        *this *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return *this;
  }
  constexpr modint operator/(const modint &rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint operator-() const noexcept { return modint(Modulus - a); }
  constexpr bool operator==(const modint &rhs) const noexcept {
    return a == rhs.a;
  }
  constexpr bool operator!=(const modint &rhs) const noexcept {
    return a != rhs.a;
  }
  constexpr bool operator!() const noexcept { return !a; }
  friend constexpr modint pow(modint rhs, long long exp) noexcept {
    modint res{1};
    while (exp) {
      if (exp & 1)
        res *= rhs;
      rhs *= rhs;
      exp >>= 1;
    }
    return res;
  }
  template <class T> friend constexpr modint operator+(T x, modint y) noexcept {
    return modint(x) + y;
  }
  template <class T> friend constexpr modint operator-(T x, modint y) noexcept {
    return modint(x) - y;
  }
  template <class T> friend constexpr modint operator*(T x, modint y) noexcept {
    return modint(x) * y;
  }
  template <class T> friend constexpr modint operator/(T x, modint y) noexcept {
    return modint(x) / y;
  }
  friend ostream &operator<<(ostream &s, const modint &rhs) noexcept {
    return s << rhs.a;
  }
  friend istream &operator>>(istream &s, modint &rhs) noexcept {
    u64 a;
    rhs = modint{(s >> a, a)};
    return s;
  }
};

using mint = modint<MOD>;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int N, K;
  cin >> N >> K;
  mint dp[N + 1][N + 1][K + 1];
  for (int i = 0; i < N + 1; ++i)
    for (int j = 0; j < N + 1; ++j)
      for (int k = 0; k < K + 1; ++k)
        dp[i][j][k] = 0;
  dp[0][0][0] = 1;
  for (int i = 0; i < N; ++i) {
    for (int j = 0; j < N + 1; ++j) {
      for (int k = 0; j + k < K + 1; ++k) {
        dp[i + 1][j][j + k] += dp[i][j][k] + dp[i][j][k] * j;
        if (1 < j)
          dp[i + 1][j - 2][j + k] += dp[i][j][k] * j * j / 4;
        if (j < N - 1)
          dp[i + 1][j + 2][j + k] += dp[i][j][k];
      }
    }
  }
  cout << dp[N][0][K] << endl;
}