Problem p02862 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
#define ll long long
#define fi first
#define se second
#define sz(a) int((a).size())
#define pb push_back
#define eb emplace_back
#define FOR(var, from, to) for (int var = (from); var <= (to); ++var)
#define rep(var, n) for (int var = 0; var < (n); ++var)
#define rep1(var, n) for (int var = 1; var <= (n); ++var)
#define repC2(vari, varj, n)                                                   \
  for (int vari = 0; vari < (n)-1; ++vari)                                     \
    for (int varj = vari + 1; varj < (n); ++varj)
#define repC3(vari, varj, vark, n)                                             \
  for (int vari = 0; vari < (n)-2; ++vari)                                     \
    for (int varj = vari + 1; varj < (n)-1; ++varj)                            \
      for (int vark = varj + 1; vark < (n); ++vark)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define tr(i, c) for (auto i = (c).begin(); i != (c).end(); ++i)
#define mset(arr, val) memset(arr, val, sizeof(arr))
#define mid(x, y) ((x) + ((y) - (x)) / 2)
#define IN(x, a, b) ((a) <= (x) && (x) <= (b))
using namespace std;
template <typename T> void Out(T x) { cout << x << endl; }
template <typename T1, typename T2> void Ans(bool f, T1 y, T2 n) {
  if (f)
    Out(y);
  else
    Out(n);
}

const int MAX = 510000;
const int MOD = 1000000007;

long long fac[MAX], finv[MAX], inv[MAX];

void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++) {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}

long long COM(int n, int k) {
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

int main() {
  COMinit();
  int X, Y;
  int time, xtime, ytime;
  ll ans = 0;
  cin >> X >> Y;
  if ((X + Y) % 3 != 0) {
    Out(0);
    return 0;
  }
  time = (X + Y) / 3;
  xtime = X - time;
  ytime = Y - time;
  ans = COM(time, xtime);

  Out(ans);
  return 0;
}

Fixed submission:
#include <bits/stdc++.h>
#define ll long long
#define fi first
#define se second
#define sz(a) int((a).size())
#define pb push_back
#define eb emplace_back
#define FOR(var, from, to) for (int var = (from); var <= (to); ++var)
#define rep(var, n) for (int var = 0; var < (n); ++var)
#define rep1(var, n) for (int var = 1; var <= (n); ++var)
#define repC2(vari, varj, n)                                                   \
  for (int vari = 0; vari < (n)-1; ++vari)                                     \
    for (int varj = vari + 1; varj < (n); ++varj)
#define repC3(vari, varj, vark, n)                                             \
  for (int vari = 0; vari < (n)-2; ++vari)                                     \
    for (int varj = vari + 1; varj < (n)-1; ++varj)                            \
      for (int vark = varj + 1; vark < (n); ++vark)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define tr(i, c) for (auto i = (c).begin(); i != (c).end(); ++i)
#define mset(arr, val) memset(arr, val, sizeof(arr))
#define mid(x, y) ((x) + ((y) - (x)) / 2)
#define IN(x, a, b) ((a) <= (x) && (x) <= (b))
using namespace std;
template <typename T> void Out(T x) { cout << x << endl; }
template <typename T1, typename T2> void Ans(bool f, T1 y, T2 n) {
  if (f)
    Out(y);
  else
    Out(n);
}

const int MAX = 5100000;
const int MOD = 1000000007;

long long fac[MAX], finv[MAX], inv[MAX];

void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++) {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}

long long COM(int n, int k) {
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

int main() {
  COMinit();
  int X, Y;
  int time, xtime, ytime;
  ll ans = 0;
  cin >> X >> Y;
  if ((X + Y) % 3 != 0) {
    Out(0);
    return 0;
  }
  time = (X + Y) / 3;
  xtime = X - time;
  ytime = Y - time;
  ans = COM(time, xtime);

  Out(ans);
  return 0;
}