Problem p04038 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;
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 Ans(f, y, n)                                                           \
  if (f)                                                                       \
    cout << y << endl;                                                         \
  else                                                                         \
    cout << n << endl;
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v)                                                              \
  cout << #v << "=" << endl;                                                   \
  REP(i, v.size()) { cout << v[i] << ","; }                                    \
  cout << endl;
#define mdebug(m)                                                              \
  cout << #m << "=" << endl;                                                   \
  REP(i, m.size()) {                                                           \
    REP(j, m[i].size()) { cout << m[i][j] << ","; }                            \
    cout << endl;                                                              \
  }
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000

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>;

template <typename T> void readv(vector<T> &a) { REP(i, a.size()) cin >> a[i]; }
void readv_m1(vector<int> &a) {
  REP(i, a.size()) {
    cin >> a[i];
    a[i]--;
  }
}

// int dx[4] = {1,0,-1,0};
// int dy[4] = {0,1,0,-1};

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];
  }
};

signed main() {

  int N, K;
  cin >> N >> K;
  if (K == 1) {
    cout << 1 << endl;
    return 0;
  }
  mmat dp(N + 1, mvec(K + 1, 0));
  dp[0][0] = 1;
  Combination C(N * K);
  REP(i, N) {
    REP(j, i + 1) {
      int n = K * i - j;
      dp[i + 1][j + 1] = dp[i][j] * C.nCr(n + K - 2, K - 2);
    }
    IREP(j, i + 1) dp[i + 1][j] += dp[i + 1][j + 1];
  }
  // mdebug(dp);
  mint ans = dp[N][0] * C.fact[N];
  cout << ans << endl;

  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
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 Ans(f, y, n)                                                           \
  if (f)                                                                       \
    cout << y << endl;                                                         \
  else                                                                         \
    cout << n << endl;
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v)                                                              \
  cout << #v << "=" << endl;                                                   \
  REP(i, v.size()) { cout << v[i] << ","; }                                    \
  cout << endl;
#define mdebug(m)                                                              \
  cout << #m << "=" << endl;                                                   \
  REP(i, m.size()) {                                                           \
    REP(j, m[i].size()) { cout << m[i][j] << ","; }                            \
    cout << endl;                                                              \
  }
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000

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>;

template <typename T> void readv(vector<T> &a) { REP(i, a.size()) cin >> a[i]; }
void readv_m1(vector<int> &a) {
  REP(i, a.size()) {
    cin >> a[i];
    a[i]--;
  }
}

// int dx[4] = {1,0,-1,0};
// int dy[4] = {0,1,0,-1};

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];
  }
};

signed main() {

  int N, K;
  cin >> N >> K;
  if (K == 1) {
    cout << 1 << endl;
    return 0;
  }
  mmat dp(N + 1, mvec(N + 1, 0));
  dp[0][0] = 1;
  Combination C(N * K);
  REP(i, N) {
    REP(j, i + 1) {
      int n = K * i - j;
      dp[i + 1][j + 1] = dp[i][j] * C.nCr(n + K - 2, K - 2);
    }
    IREP(j, i + 1) dp[i + 1][j] += dp[i + 1][j + 1];
  }
  // mdebug(dp);
  mint ans = dp[N][0] * C.fact[N];
  cout << ans << endl;

  return 0;
}