Problem p02862 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;

#define INF_LL (int64)1e18
#define INF (int32)1e9
#define REP(i, n) for (int64 i = 0; i < (n); i++)
#define FOR(i, a, b) for (int64 i = (a); i < (b); i++)
#define all(x) x.begin(), x.end()
#define fs first
#define sc second

using int32 = int_fast32_t;
using uint32 = uint_fast32_t;
using int64 = int_fast64_t;
using uint64 = uint_fast64_t;
using PII = pair<int32, int32>;
using PLL = pair<int64, int64>;

const double eps = 1e-10;

template <typename A, typename B> inline void chmin(A &a, B b) {
  if (a > b)
    a = b;
}
template <typename A, typename B> inline void chmax(A &a, B b) {
  if (a < b)
    a = b;
}

template <typename T> vector<T> make_v(size_t a) { return vector<T>(a); }

template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename U, typename... V>
typename enable_if<is_same<T, U>::value != 0>::type fill_v(U &u, const V... v) {
  u = U(v...);
}

template <typename T, typename U, typename... V>
typename enable_if<is_same<T, U>::value == 0>::type fill_v(U &u, const V... v) {
  for (auto &e : u)
    fill_v<T>(e, v...);
}

template <::std::uint_fast64_t mod> class ModInt {
private:
  using value_type = ::std::uint_fast64_t;
  value_type n;

public:
  ModInt() : n(0) {}
  ModInt(value_type n_) : n(n_ % mod) {}
  ModInt(const ModInt &m) : n(m.n) {}

  template <typename T> explicit operator T() const {
    return static_cast<T>(n);
  }
  value_type get() const { return n; }

  friend ::std::ostream &operator<<(::std::ostream &os, const ModInt<mod> &a) {
    return os << a.n;
  }

  friend ::std::istream &operator>>(::std::istream &is, ModInt<mod> &a) {
    value_type x;
    is >> x;
    a = ModInt<mod>(x);
    return is;
  }

  bool operator==(const ModInt &m) const { return n == m.n; }
  bool operator!=(const ModInt &m) const { return n != m.n; }
  ModInt &operator*=(const ModInt &m) {
    n = n * m.n % mod;
    return *this;
  }

  ModInt pow(value_type b) const {
    ModInt ans = 1, m = ModInt(*this);
    while (b) {
      if (b & 1)
        ans *= m;
      m *= m;
      b >>= 1;
    }
    return ans;
  }

  ModInt inv() const { return (*this).pow(mod - 2); }
  ModInt &operator+=(const ModInt &m) {
    n += m.n;
    n = (n < mod ? n : n - mod);
    return *this;
  }
  ModInt &operator-=(const ModInt &m) {
    n += mod - m.n;
    n = (n < mod ? n : n - mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &m) {
    *this *= m.inv();
    return *this;
  }
  ModInt operator+(const ModInt &m) const { return ModInt(*this) += m; }
  ModInt operator-(const ModInt &m) const { return ModInt(*this) -= m; }
  ModInt operator*(const ModInt &m) const { return ModInt(*this) *= m; }
  ModInt operator/(const ModInt &m) const { return ModInt(*this) /= m; }
  ModInt &operator++() {
    n += 1;
    return *this;
  }
  ModInt &operator--() {
    n -= 1;
    return *this;
  }
  ModInt operator++(int) {
    ModInt old(n);
    n += 1;
    return old;
  }
  ModInt operator--(int) {
    ModInt old(n);
    n -= 1;
    return old;
  }
  ModInt operator-() const { return ModInt(mod - n); }
};

template <::std::size_t size, ::std::uint_fast64_t mod = 1000000007>
class Factorial {
private:
  using value_type = ModInt<mod>;
  ::std::vector<value_type> fact, inv;

public:
  Factorial() : fact(size + 1, 1), inv(size + 1, 1) {
    for (::std::size_t i = 1; i <= size; ++i) {
      fact[i] = fact[i - 1] * value_type(i);
      inv[i] = fact[i].inv();
    }
  }

  value_type comb(::std::int64_t a, ::std::int64_t b) {
    assert(a >= b);
    assert(b >= 0);
    return fact[a] * inv[b] * inv[a - b];
  }

  value_type &operator[](::std::size_t k) { return fact[k]; }
};

constexpr int64 mod = 1e9 + 7;
using Mint = ModInt<mod>;
Factorial<2123456> f;

int main(void) {
  int64 X, Y;
  cin >> X >> Y;
  Mint res = 0;
  REP(i, X + Y + 1) {
    int64 x = X - i, y = Y - i;
    if (x + y != i)
      continue;
    res += f.comb(x + y, x);
  }
  cout << res << endl;
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;

#define INF_LL (int64)1e18
#define INF (int32)1e9
#define REP(i, n) for (int64 i = 0; i < (n); i++)
#define FOR(i, a, b) for (int64 i = (a); i < (b); i++)
#define all(x) x.begin(), x.end()
#define fs first
#define sc second

using int32 = int_fast32_t;
using uint32 = uint_fast32_t;
using int64 = int_fast64_t;
using uint64 = uint_fast64_t;
using PII = pair<int32, int32>;
using PLL = pair<int64, int64>;

const double eps = 1e-10;

template <typename A, typename B> inline void chmin(A &a, B b) {
  if (a > b)
    a = b;
}
template <typename A, typename B> inline void chmax(A &a, B b) {
  if (a < b)
    a = b;
}

template <typename T> vector<T> make_v(size_t a) { return vector<T>(a); }

template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename U, typename... V>
typename enable_if<is_same<T, U>::value != 0>::type fill_v(U &u, const V... v) {
  u = U(v...);
}

template <typename T, typename U, typename... V>
typename enable_if<is_same<T, U>::value == 0>::type fill_v(U &u, const V... v) {
  for (auto &e : u)
    fill_v<T>(e, v...);
}

template <::std::uint_fast64_t mod> class ModInt {
private:
  using value_type = ::std::uint_fast64_t;
  value_type n;

public:
  ModInt() : n(0) {}
  ModInt(value_type n_) : n(n_ % mod) {}
  ModInt(const ModInt &m) : n(m.n) {}

  template <typename T> explicit operator T() const {
    return static_cast<T>(n);
  }
  value_type get() const { return n; }

  friend ::std::ostream &operator<<(::std::ostream &os, const ModInt<mod> &a) {
    return os << a.n;
  }

  friend ::std::istream &operator>>(::std::istream &is, ModInt<mod> &a) {
    value_type x;
    is >> x;
    a = ModInt<mod>(x);
    return is;
  }

  bool operator==(const ModInt &m) const { return n == m.n; }
  bool operator!=(const ModInt &m) const { return n != m.n; }
  ModInt &operator*=(const ModInt &m) {
    n = n * m.n % mod;
    return *this;
  }

  ModInt pow(value_type b) const {
    ModInt ans = 1, m = ModInt(*this);
    while (b) {
      if (b & 1)
        ans *= m;
      m *= m;
      b >>= 1;
    }
    return ans;
  }

  ModInt inv() const { return (*this).pow(mod - 2); }
  ModInt &operator+=(const ModInt &m) {
    n += m.n;
    n = (n < mod ? n : n - mod);
    return *this;
  }
  ModInt &operator-=(const ModInt &m) {
    n += mod - m.n;
    n = (n < mod ? n : n - mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &m) {
    *this *= m.inv();
    return *this;
  }
  ModInt operator+(const ModInt &m) const { return ModInt(*this) += m; }
  ModInt operator-(const ModInt &m) const { return ModInt(*this) -= m; }
  ModInt operator*(const ModInt &m) const { return ModInt(*this) *= m; }
  ModInt operator/(const ModInt &m) const { return ModInt(*this) /= m; }
  ModInt &operator++() {
    n += 1;
    return *this;
  }
  ModInt &operator--() {
    n -= 1;
    return *this;
  }
  ModInt operator++(int) {
    ModInt old(n);
    n += 1;
    return old;
  }
  ModInt operator--(int) {
    ModInt old(n);
    n -= 1;
    return old;
  }
  ModInt operator-() const { return ModInt(mod - n); }
};

template <::std::size_t size, ::std::uint_fast64_t mod = 1000000007>
class Factorial {
private:
  using value_type = ModInt<mod>;
  ::std::vector<value_type> fact, inv;

public:
  Factorial() : fact(size + 1, 1), inv(size + 1, 1) {
    for (::std::size_t i = 1; i <= size; ++i) {
      fact[i] = fact[i - 1] * value_type(i);
      inv[i] = fact[i].inv();
    }
  }

  value_type comb(::std::int64_t a, ::std::int64_t b) {
    assert(a >= b);
    assert(b >= 0);
    return fact[a] * inv[b] * inv[a - b];
  }

  value_type &operator[](::std::size_t k) { return fact[k]; }
};

constexpr int64 mod = 1e9 + 7;
using Mint = ModInt<mod>;
Factorial<2123456> f;

int main(void) {
  int64 X, Y;
  cin >> X >> Y;
  Mint res = 0;
  REP(i, min(X, Y) + 1) {
    int64 x = X - i, y = Y - i;
    if (x + y != i)
      continue;
    res += f.comb(x + y, x);
  }
  cout << res << endl;
}