Problem p03832 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <string>
#include <tuple>
#include <vector>
#define mkp make_pair
#define mkt make_tuple
#define rep(i, n) for (int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;
const ll MOD = 1e9 + 7;

#define MAX_N 2002
ll inv[MAX_N + 10], fac[MAX_N + 10], ifac[MAX_N + 10];

void setComb() {
  inv[0] = 1;
  inv[1] = 1;
  fac[1] = 1;
  ifac[1] = 1;
  fac[0] = 1;
  ifac[0] = 1;
  for (int i = 2; i < MAX_N; i++) {
    inv[i] = (-MOD / i) * inv[MOD % i] % MOD;
    fac[i] = fac[i - 1] * i % MOD;
    ifac[i] = ifac[i - 1] * inv[i] % MOD;

    inv[i] = (inv[i] + MOD) % MOD;
    fac[i] = (fac[i] + MOD) % MOD;
    ifac[i] = (ifac[i] + MOD) % MOD;
  }
  return;
}

ll comb(ll n, ll k) {
  if (n < k || n < 0 || k < 0)
    return 0;
  else
    return ((fac[n] * ifac[k] % MOD * ifac[n - k] % MOD + MOD) % MOD);
}

ll hcomb(ll n, ll r) {
  if (n == 0 && r == 0)
    return 1;
  else if (n < 0 || r < 0)
    return 0;
  else
    return comb(n + r - 1, r - 1);
}

int N, A, B, C, D;
ll dp[1001][1001];

ll coef[1001];

void add(ll &a, ll b) { a = (a + b) % MOD; }

void mul(ll &a, ll b) { a = a * b % MOD; }

ll rec(int ma, int rest) {
  if (rest == 0)
    return 1;
  if (ma < A)
    return 0;
  if (dp[ma][rest] >= 0)
    return dp[ma][rest];

  ll res = 0;
  add(res, rec(ma - 1, rest));

  ll c = coef[ma];
  for (int i = C; i <= D; i++) {
    if (i * ma > rest)
      break;

    if (i > C)
      mul(c, comb(i * ma, ma));
    ll cost = c;
    mul(cost, comb(rest, i * ma));
    mul(cost, ifac[i]);

    ll tmp = rec(ma - 1, rest - (i * ma));
    mul(tmp, cost);
    add(res, tmp);
  }
  return dp[ma][rest] = res;
}

int main() {
  cin >> N >> A >> B >> C >> D;

  for (int i = 0; i <= N; i++)
    for (int j = 0; j <= N; j++)
      dp[i][j] = -1;

  setComb();
  for (int i = A; i <= B; i++) {
    coef[i] = 1;
    for (int j = 0; j < C; j++) {
      mul(coef[i], comb(i * C - i * j, i));
    }
  }

  cout << rec(B, N) << endl;

  return 0;
}


Fixed submission:
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <string>
#include <tuple>
#include <vector>
#define mkp make_pair
#define mkt make_tuple
#define rep(i, n) for (int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;
const ll MOD = 1e9 + 7;

#define MAX_N 2002
ll inv[MAX_N + 10], fac[MAX_N + 10], ifac[MAX_N + 10];

void setComb() {
  inv[0] = 1;
  inv[1] = 1;
  fac[1] = 1;
  ifac[1] = 1;
  fac[0] = 1;
  ifac[0] = 1;
  for (int i = 2; i < MAX_N; i++) {
    inv[i] = (-MOD / i) * inv[MOD % i] % MOD;
    fac[i] = fac[i - 1] * i % MOD;
    ifac[i] = ifac[i - 1] * inv[i] % MOD;

    inv[i] = (inv[i] + MOD) % MOD;
    fac[i] = (fac[i] + MOD) % MOD;
    ifac[i] = (ifac[i] + MOD) % MOD;
  }
  return;
}

ll comb(ll n, ll k) {
  if (n < k || n < 0 || k < 0)
    return 0;
  else
    return ((fac[n] * ifac[k] % MOD * ifac[n - k] % MOD + MOD) % MOD);
}

ll hcomb(ll n, ll r) {
  if (n == 0 && r == 0)
    return 1;
  else if (n < 0 || r < 0)
    return 0;
  else
    return comb(n + r - 1, r - 1);
}

int N, A, B, C, D;
ll dp[1001][1001];

ll coef[1001];

void add(ll &a, ll b) { a = (a + b) % MOD; }

void mul(ll &a, ll b) { a = a * b % MOD; }

ll rec(int ma, int rest) {
  if (rest == 0)
    return 1;
  if (ma < A)
    return 0;
  if (dp[ma][rest] >= 0)
    return dp[ma][rest];

  ll res = 0;
  add(res, rec(ma - 1, rest));

  ll c = coef[ma];
  for (int i = C; i <= D; i++) {
    if (i * ma > rest)
      break;

    if (i > C)
      mul(c, comb(i * ma, ma));
    ll cost = c;
    mul(cost, comb(rest, i * ma));
    mul(cost, ifac[i]);

    ll tmp = rec(ma - 1, rest - (i * ma));
    mul(tmp, cost);
    add(res, tmp);
  }
  return dp[ma][rest] = res;
}

int main() {
  cin >> N >> A >> B >> C >> D;

  for (int i = 0; i <= N; i++)
    for (int j = 0; j <= N; j++)
      dp[i][j] = -1;

  setComb();
  for (int i = A; i <= B; i++) {
    coef[i] = 1;
    if (i * C > N)
      break;
    for (int j = 0; j < C; j++) {
      mul(coef[i], comb(i * C - i * j, i));
    }
  }

  cout << rec(B, N) << endl;

  return 0;
}