Problem p01452 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <array>
#include <assert.h>
#include <bitset>
#include <complex>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <math.h>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <stdio.h>
#include <string.h>
#include <string>
#include <vector>
using namespace std;

const int mod = 1000000007;
struct Mod {
public:
  int num;
  Mod() : num(0) { ; }
  Mod(long long int n) : num((n % mod + mod) % mod) { ; }
  Mod(int n) : num((n % mod + mod) % mod) { ; }
  operator int() { return num; }
};

Mod operator+(const Mod a, const Mod b) { return Mod((a.num + b.num) % mod); }
Mod operator+(const long long int a, const Mod b) { return Mod(a) + b; }
Mod operator++(Mod &a) { return a + Mod(1); }
Mod operator-(const Mod a, const Mod b) {
  return Mod((mod + a.num - b.num) % mod);
}
Mod operator-(const long long int a, const Mod b) { return Mod(a) - b; }
Mod operator--(Mod &a) { return a - Mod(1); }
Mod operator*(const Mod a, const Mod b) {
  return Mod(((long long)a.num * b.num) % mod);
}
Mod operator*(const long long int a, const Mod b) { return Mod(a) * b; }
Mod operator+=(Mod &a, const Mod b) { return a = a + b; }
Mod operator+=(long long int &a, const Mod b) { return a = a + b; }
Mod operator-=(Mod &a, const Mod b) { return a = a - b; }
Mod operator-=(long long int &a, const Mod b) { return a = a - b; }
Mod operator*=(Mod &a, const Mod b) { return a = a * b; }
Mod operator*=(long long int &a, const Mod b) { return a = a * b; }
Mod operator^(const Mod a, const int n) {
  if (n == 0)
    return Mod(1);
  Mod res = (a * a) ^ (n / 2);
  if (n % 2)
    res = res * a;
  return res;
}
Mod inv(const Mod a) { return a ^ (mod - 2); }
Mod operator/(const Mod a, const Mod b) {
  assert(b.num != 0);
  return a * inv(b);
}
Mod operator/(const long long int a, const Mod b) {
  assert(b.num != 0);
  return Mod(a) * inv(b);
}
Mod operator/=(Mod &a, const Mod b) {
  assert(b.num != 0);
  return a = a * inv(b);
}

#define MAX_N 102400

Mod fact[MAX_N], factinv[MAX_N];
void init() {
  fact[0] = Mod(1);
  factinv[0] = 1;
  for (int i = 0; i < MAX_N - 1; ++i) {
    fact[i + 1] = fact[i] * Mod(i + 1);
    factinv[i + 1] = factinv[i] / Mod(i + 1);
  }
}
Mod comb(const int a, const int b) {
  return fact[a] * factinv[b] * factinv[a - b];
}

Mod getans(int m, int p) {
  if (m == 0)
    return 1;
  Mod bb(comb(p + m, m) - comb(p + m, m - 1));
  return comb(p + m, m) - comb(p + m, m - 1);
}

int main() {
  init();
  int N, M, K;
  cin >> N >> M >> K;
  Mod totalans(0);
  for (int pxtime = N; pxtime <= N + K; ++pxtime) {
    int mxtime = pxtime - N;
    int pytime = M + (K - pxtime + N);
    int mytime = K - pxtime + N;
    Mod ans(1);
    ans *= getans(mxtime, pxtime);
    ans *= getans(mytime, pytime);
    ans *= comb(N + M + 2 * K, pxtime + mxtime);
    totalans += ans;
  }
  cout << totalans << endl;
  return 0;
}

Fixed submission:
#include <algorithm>
#include <array>
#include <assert.h>
#include <bitset>
#include <complex>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <math.h>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <stdio.h>
#include <string.h>
#include <string>
#include <vector>
using namespace std;

const int mod = 1000000007;
struct Mod {
public:
  int num;
  Mod() : num(0) { ; }
  Mod(long long int n) : num((n % mod + mod) % mod) { ; }
  Mod(int n) : num((n % mod + mod) % mod) { ; }
  operator int() { return num; }
};

Mod operator+(const Mod a, const Mod b) { return Mod((a.num + b.num) % mod); }
Mod operator+(const long long int a, const Mod b) { return Mod(a) + b; }
Mod operator++(Mod &a) { return a + Mod(1); }
Mod operator-(const Mod a, const Mod b) {
  return Mod((mod + a.num - b.num) % mod);
}
Mod operator-(const long long int a, const Mod b) { return Mod(a) - b; }
Mod operator--(Mod &a) { return a - Mod(1); }
Mod operator*(const Mod a, const Mod b) {
  return Mod(((long long)a.num * b.num) % mod);
}
Mod operator*(const long long int a, const Mod b) { return Mod(a) * b; }
Mod operator+=(Mod &a, const Mod b) { return a = a + b; }
Mod operator+=(long long int &a, const Mod b) { return a = a + b; }
Mod operator-=(Mod &a, const Mod b) { return a = a - b; }
Mod operator-=(long long int &a, const Mod b) { return a = a - b; }
Mod operator*=(Mod &a, const Mod b) { return a = a * b; }
Mod operator*=(long long int &a, const Mod b) { return a = a * b; }
Mod operator^(const Mod a, const int n) {
  if (n == 0)
    return Mod(1);
  Mod res = (a * a) ^ (n / 2);
  if (n % 2)
    res = res * a;
  return res;
}
Mod inv(const Mod a) { return a ^ (mod - 2); }
Mod operator/(const Mod a, const Mod b) {
  assert(b.num != 0);
  return a * inv(b);
}
Mod operator/(const long long int a, const Mod b) {
  assert(b.num != 0);
  return Mod(a) * inv(b);
}
Mod operator/=(Mod &a, const Mod b) {
  assert(b.num != 0);
  return a = a * inv(b);
}

#define MAX_N 1024000

Mod fact[MAX_N], factinv[MAX_N];
void init() {
  fact[0] = Mod(1);
  factinv[0] = 1;
  for (int i = 0; i < MAX_N - 1; ++i) {
    fact[i + 1] = fact[i] * Mod(i + 1);
    factinv[i + 1] = factinv[i] / Mod(i + 1);
  }
}
Mod comb(const int a, const int b) {
  return fact[a] * factinv[b] * factinv[a - b];
}

Mod getans(int m, int p) {
  if (m == 0)
    return 1;
  Mod bb(comb(p + m, m) - comb(p + m, m - 1));
  return comb(p + m, m) - comb(p + m, m - 1);
}

int main() {
  init();
  int N, M, K;
  cin >> N >> M >> K;
  Mod totalans(0);
  for (int pxtime = N; pxtime <= N + K; ++pxtime) {
    int mxtime = pxtime - N;
    int pytime = M + (K - pxtime + N);
    int mytime = K - pxtime + N;
    Mod ans(1);
    ans *= getans(mxtime, pxtime);
    ans *= getans(mytime, pytime);
    ans *= comb(N + M + 2 * K, pxtime + mxtime);
    totalans += ans;
  }
  cout << totalans << endl;
  return 0;
}