Problem p04004 (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 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};

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

int modpow(int x, int n, int m) {
  int a = 1;
  IREP(i, 64) {
    a = (a * a) % m;
    if (((n >> i) & 1) == 1)
      a = (a * x) % m;
  }
  return a;
}

class Combination {
public:
  vec fact, invfact;
  int MAX_N, mod;

  Combination(int MAX_N, int mod) : MAX_N(MAX_N), mod(mod) { initialize(); }

  void initialize() {
    fact = vec(MAX_N + 1);
    invfact = vec(MAX_N + 1);
    fact[0] = 1;
    FOR(i, 1, MAX_N + 1) { fact[i] = (fact[i - 1] * i) % mod; }
    invfact[MAX_N] = modpow(fact[MAX_N], mod - 2, mod);
    IREP(i, MAX_N) { invfact[i] = (invfact[i + 1] * (i + 1)) % mod; }
  }

  int nCr(int n, int r) {
    if (r > n || r < 0 || n < 0)
      return 0;
    if (n > MAX_N) {
      MAX_N = n;
      initialize();
    }
    int a = fact[n];
    a = (a * invfact[r]) % mod;
    a = (a * invfact[n - r]) % mod;
    return a;
  }

  int nPr(int n, int r) {
    if (r > n || r < 0 || n < 0)
      return 0;
    if (n > MAX_N) {
      MAX_N = n;
      initialize();
    }
    int a = fact[n];
    a = (a * invfact[n - r]) % mod;
    return a;
  }
};

signed main() {

  int N, M, K;
  cin >> N >> M >> K;
  assert(N <= 1000 && M <= 1000 && K <= 1000);

  int ans = 0;
  Combination C(N + M + K, mod);
  int c = 1;
  REP(i, M + K + 1) {
    if (i > 0) {
      Mult(c, 2);
      if (i - 1 >= M + 1)
        Add(c, C.nCr(i - 1, M + 1));
      if (i - 1 - K - 1 >= 0)
        Add(c, C.nCr(i - 1, i - 1 - K - 1));
      if (i >= M + 1)
        Add(c, mod - C.nCr(i, M + 1));
      if (i - K - 1 >= 0)
        Add(c, mod - C.nCr(i, i - K - 1));
    }
    int tmp = (c * C.nCr(N - 1 + i, i)) % mod;
    Add(ans, tmp * modpow(3, M + K - i, mod));
  }
  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 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};

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

int modpow(int x, int n, int m) {
  int a = 1;
  IREP(i, 64) {
    a = (a * a) % m;
    if (((n >> i) & 1) == 1)
      a = (a * x) % m;
  }
  return a;
}

class Combination {
public:
  vec fact, invfact;
  int MAX_N, mod;

  Combination(int MAX_N, int mod) : MAX_N(MAX_N), mod(mod) { initialize(); }

  void initialize() {
    fact = vec(MAX_N + 1);
    invfact = vec(MAX_N + 1);
    fact[0] = 1;
    FOR(i, 1, MAX_N + 1) { fact[i] = (fact[i - 1] * i) % mod; }
    invfact[MAX_N] = modpow(fact[MAX_N], mod - 2, mod);
    IREP(i, MAX_N) { invfact[i] = (invfact[i + 1] * (i + 1)) % mod; }
  }

  int nCr(int n, int r) {
    if (r > n || r < 0 || n < 0)
      return 0;
    if (n > MAX_N) {
      MAX_N = n;
      initialize();
    }
    int a = fact[n];
    a = (a * invfact[r]) % mod;
    a = (a * invfact[n - r]) % mod;
    return a;
  }

  int nPr(int n, int r) {
    if (r > n || r < 0 || n < 0)
      return 0;
    if (n > MAX_N) {
      MAX_N = n;
      initialize();
    }
    int a = fact[n];
    a = (a * invfact[n - r]) % mod;
    return a;
  }
};

signed main() {

  int N, M, K;
  cin >> N >> M >> K;

  int ans = 0;
  Combination C(N + M + K, mod);
  int c = 1;
  REP(i, M + K + 1) {
    if (i > 0) {
      Mult(c, 2);
      if (i - 1 >= M + 1)
        Add(c, C.nCr(i - 1, M + 1));
      if (i - 1 - K - 1 >= 0)
        Add(c, C.nCr(i - 1, i - 1 - K - 1));
      if (i >= M + 1)
        Add(c, mod - C.nCr(i, M + 1));
      if (i - K - 1 >= 0)
        Add(c, mod - C.nCr(i, i - K - 1));
    }
    int tmp = (c * C.nCr(N - 1 + i, i)) % mod;
    Add(ans, tmp * modpow(3, M + K - i, mod));
  }
  cout << ans << endl;

  return 0;
}