Problem p02862 (C++)

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

#define rep(i, n) for (int(i) = 0; (i) < (int)(n); (i)++)
#define frep(i, m, n) for (int(i) = (m); (i) < (int)(n); (i)++)
#define rrep(i, n) for (int(i) = (n)-1; (i) > -1; (i)--)
#define frrep(i, m, n) for (int(i) = (n)-1; (i) > (int)(m)-1; (i)--)
#define ALL(x) (x).begin(), (x).end()
#define SQR(x) (x) * (x)
#define CEIL(a, b) ((a) + (b)-1) / (b)

typedef long long ll;
const int INF = 1001001001;
const int MOD = 1000000007;
const int MAX_N = 101010;

// A:array of pair, N:size of array
void sort_second(vector<pair<ll, ll>> &A, int N);
// a^n
ll a_n(ll a, ll n);
// make vector of (n!)%MOD, (n!)^(-1)%MOD to calculate nCk
void factorial_map(vector<ll> &n, vector<ll> &ninv);
// a^(-1) % MOD
ll inv(ll a);
// map of prime factorization
void prime_map(map<int, int> &a, int n);
// list of prime (is_prime.size() = n + 1, primes.size() = 0)
void prime_list(int n, vector<int> &primes, vector<bool> &is_prime);
// get gcd from prime map
ll gcd_map(map<int, int> a, map<int, int> b);
// get lcm from prime map
ll lcm_map(map<int, int> a, map<int, int> b);
// get gcd
ll my_gcd(ll a, ll b);
// calculate nCk
ll nCk(ll n, ll k);
// get abs
ll my_abs(ll a);

class Unionfind {
public:
  vector<ll> par, siz, rank;
  Unionfind();
  ll root(ll x);
  void merge(ll x, ll y);
  bool issame(ll x, ll y);
  ll size(ll x);
};

int main() {
  ll x, y;
  cin >> x >> y;
  if ((-1 * x + 2 * y) % 3 != 0 || (2 * x - y) % 3 != 0) {
    cout << 0 << endl;
  } else {
    ll a, b, ret;
    a = (-1 * x + 2 * y) / 3;
    b = (2 * x - y) / 3;
    vector<ll> n(1000005), ninv(1000005);
    factorial_map(n, ninv);
    ret = (n.at(a + b) * ninv.at(a)) % MOD;
    ret = (ret * ninv.at(b)) % MOD;
    cout << ret << endl;
  }
  return 0;
}

void sort_second(vector<pair<ll, ll>> &A, int N) {
  rep(i, N) swap(A.at(i).first, A.at(i).second);
  sort(ALL(A));
  rep(i, N) swap(A.at(i).first, A.at(i).second);
}
ll a_n(ll a, ll n) {
  if (n == 0)
    return 1;

  ll ret = a, count = 1;
  while (count * 2 < n) {
    ret *= ret;
    ret %= MOD;
    count *= 2;
  }
  if (count == n)
    return ret;
  else
    return (ret * a_n(a, n - count)) % MOD;
}

/* calculate a^n with no recursive process (%MOD)
ll a_n(ll a, ll n) {
    ll ret = a, count = 1;
    int num = 1;
    vector<ll> memory(100);
    memory.at(0) = a;

    while(count * 2 < n) {
        ret *= ret;
        ret %= MOD;
        count *= 2;
        memory.at(num) = ret;
        num++;
    }
    if(count == n) return ret;
    else {
        bitset<100> bit = bitset<100>(n-count);
        rep(i, 100) {
            if(bit.test(i)) ret = (ret * memory.at(i)) % MOD;
        }
        return ret;
    }
}
*/

void factorial_map(vector<ll> &n, vector<ll> &ninv) {
  n[0] = 1;
  for (int i = 1; i < n.size(); i++)
    n[i] = (n[i - 1] * i) % MOD;
  ninv[n.size() - 1] = inv(n[n.size() - 1]);
  for (int i = n.size() - 2; i > -1; i--)
    ninv[i] = (ninv[i + 1] * (i + 1)) % MOD;
}

ll inv(ll a) { return a_n(a, MOD - 2); }

void prime_map(map<int, int> &a, int n) {
  while ((n % 2) == 0) {
    n /= 2;
    if (a.count(2))
      a.at(2)++;
    else
      a[2] = 1;
  }
  for (int i = 3; i * i <= n; i += 2) {
    while ((n % i) == 0) {
      n /= i;
      if (a.count(i))
        a.at(i)++;
      else
        a[i] = 1;
    }
  }
  if (n != 1)
    a[n] = 1;
}

ll gcd_map(map<int, int> a, map<int, int> b) {
  ll ret = 1;
  for (auto p : a) {
    auto key = p.first;
    auto value = p.second;
    if (b.count(key)) {
      if (value > b.at(key))
        ret *= a_n(key, b.at(key));
      else
        ret *= a_n(key, value);
    }
  }
  return ret;
}

ll lcm_map(map<int, int> a, map<int, int> b) {
  ll ret = 1;
  for (auto p : a) {
    auto key = p.first;
    auto value = p.second;
    if (b.count(key)) {
      if (value > b.at(key))
        ret *= a_n(key, value);
      else
        ret *= a_n(key, b.at(key));
    } else {
      ret *= a_n(key, value);
    }
  }
  for (auto p : b) {
    auto key = p.first;
    auto value = p.second;
    if (a.count(key)) {
      continue;
    } else {
      ret *= a_n(key, value);
    }
  }
  return ret;
}

ll my_gcd(ll a, ll b) {
  if (b == 0)
    return a;
  return my_gcd(b, a % b);
}

ll nCk(ll n, ll k) {
  ll kfac = 1, ret = 1;
  for (int i = 1; i <= k; i++) {
    kfac = (kfac * i) % MOD;
  }
  for (int i = n; i >= n - k + 1; i--) {
    ret = (ret * i) % MOD;
  }
  ret = (ret * inv(kfac)) % MOD;
  return ret;
}

void prime_list(int n, vector<int> &primes, vector<bool> &is_prime) {
  int p = 0;
  rep(i, n + 1) is_prime[i] = true;
  is_prime[0] = false;
  is_prime[1] = false;
  for (int i = 2; i <= n; i++) {
    if (is_prime[i]) {
      primes.push_back(i);
      for (int j = 2 * i; j <= n; j += i)
        is_prime[j] = false;
    }
  }
}

ll my_abs(ll a) {
  if (a >= 0)
    return a;
  else
    return -1 * a;
}

Unionfind::Unionfind() {
  par.resize(MAX_N);
  siz.resize(MAX_N);
  rank.resize(MAX_N);
  rep(i, MAX_N) {
    par[i] = i;
    siz[i] = 1;
    rank[i] = 0;
  }
}
ll Unionfind::root(ll x) {
  if (par[x] == x)
    return x;
  else {
    return par[x] = root(par[x]);
  }
}
void Unionfind::merge(ll x, ll y) {
  x = root(x);
  y = root(y);
  if (x == y)
    return;
  if (rank[x] < rank[y]) {
    par[x] = y;
    siz[y] += siz[x];
  } else {
    par[y] = x;
    siz[x] += siz[y];
    if (rank[x] == rank[y])
      rank[x]++;
  }
}
bool Unionfind::issame(ll x, ll y) { return root(x) == root(y); }
ll Unionfind::size(ll x) { return siz[root(x)]; }

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

#define rep(i, n) for (int(i) = 0; (i) < (int)(n); (i)++)
#define frep(i, m, n) for (int(i) = (m); (i) < (int)(n); (i)++)
#define rrep(i, n) for (int(i) = (n)-1; (i) > -1; (i)--)
#define frrep(i, m, n) for (int(i) = (n)-1; (i) > (int)(m)-1; (i)--)
#define ALL(x) (x).begin(), (x).end()
#define SQR(x) (x) * (x)
#define CEIL(a, b) ((a) + (b)-1) / (b)

typedef long long ll;
const int INF = 1001001001;
const int MOD = 1000000007;
const int MAX_N = 101010;

// A:array of pair, N:size of array
void sort_second(vector<pair<ll, ll>> &A, int N);
// a^n
ll a_n(ll a, ll n);
// make vector of (n!)%MOD, (n!)^(-1)%MOD to calculate nCk
void factorial_map(vector<ll> &n, vector<ll> &ninv);
// a^(-1) % MOD
ll inv(ll a);
// map of prime factorization
void prime_map(map<int, int> &a, int n);
// list of prime (is_prime.size() = n + 1, primes.size() = 0)
void prime_list(int n, vector<int> &primes, vector<bool> &is_prime);
// get gcd from prime map
ll gcd_map(map<int, int> a, map<int, int> b);
// get lcm from prime map
ll lcm_map(map<int, int> a, map<int, int> b);
// get gcd
ll my_gcd(ll a, ll b);
// calculate nCk
ll nCk(ll n, ll k);
// get abs
ll my_abs(ll a);

class Unionfind {
public:
  vector<ll> par, siz, rank;
  Unionfind();
  ll root(ll x);
  void merge(ll x, ll y);
  bool issame(ll x, ll y);
  ll size(ll x);
};

int main() {
  ll x, y;
  cin >> x >> y;
  if ((-1 * x + 2 * y) % 3 != 0 || (2 * x - y) % 3 != 0 || -1 * x + 2 * y < 0 ||
      2 * x - y < 0) {
    cout << 0 << endl;
  } else {
    ll a, b, ret;
    a = (-1 * x + 2 * y) / 3;
    b = (2 * x - y) / 3;
    vector<ll> n(1000005), ninv(1000005);
    factorial_map(n, ninv);
    ret = (n.at(a + b) * ninv.at(a)) % MOD;
    ret = (ret * ninv.at(b)) % MOD;
    cout << ret << endl;
  }
  return 0;
}

void sort_second(vector<pair<ll, ll>> &A, int N) {
  rep(i, N) swap(A.at(i).first, A.at(i).second);
  sort(ALL(A));
  rep(i, N) swap(A.at(i).first, A.at(i).second);
}
ll a_n(ll a, ll n) {
  if (n == 0)
    return 1;

  ll ret = a, count = 1;
  while (count * 2 < n) {
    ret *= ret;
    ret %= MOD;
    count *= 2;
  }
  if (count == n)
    return ret;
  else
    return (ret * a_n(a, n - count)) % MOD;
}

/* calculate a^n with no recursive process (%MOD)
ll a_n(ll a, ll n) {
    ll ret = a, count = 1;
    int num = 1;
    vector<ll> memory(100);
    memory.at(0) = a;

    while(count * 2 < n) {
        ret *= ret;
        ret %= MOD;
        count *= 2;
        memory.at(num) = ret;
        num++;
    }
    if(count == n) return ret;
    else {
        bitset<100> bit = bitset<100>(n-count);
        rep(i, 100) {
            if(bit.test(i)) ret = (ret * memory.at(i)) % MOD;
        }
        return ret;
    }
}
*/

void factorial_map(vector<ll> &n, vector<ll> &ninv) {
  n[0] = 1;
  for (int i = 1; i < n.size(); i++)
    n[i] = (n[i - 1] * i) % MOD;
  ninv[n.size() - 1] = inv(n[n.size() - 1]);
  for (int i = n.size() - 2; i > -1; i--)
    ninv[i] = (ninv[i + 1] * (i + 1)) % MOD;
}

ll inv(ll a) { return a_n(a, MOD - 2); }

void prime_map(map<int, int> &a, int n) {
  while ((n % 2) == 0) {
    n /= 2;
    if (a.count(2))
      a.at(2)++;
    else
      a[2] = 1;
  }
  for (int i = 3; i * i <= n; i += 2) {
    while ((n % i) == 0) {
      n /= i;
      if (a.count(i))
        a.at(i)++;
      else
        a[i] = 1;
    }
  }
  if (n != 1)
    a[n] = 1;
}

ll gcd_map(map<int, int> a, map<int, int> b) {
  ll ret = 1;
  for (auto p : a) {
    auto key = p.first;
    auto value = p.second;
    if (b.count(key)) {
      if (value > b.at(key))
        ret *= a_n(key, b.at(key));
      else
        ret *= a_n(key, value);
    }
  }
  return ret;
}

ll lcm_map(map<int, int> a, map<int, int> b) {
  ll ret = 1;
  for (auto p : a) {
    auto key = p.first;
    auto value = p.second;
    if (b.count(key)) {
      if (value > b.at(key))
        ret *= a_n(key, value);
      else
        ret *= a_n(key, b.at(key));
    } else {
      ret *= a_n(key, value);
    }
  }
  for (auto p : b) {
    auto key = p.first;
    auto value = p.second;
    if (a.count(key)) {
      continue;
    } else {
      ret *= a_n(key, value);
    }
  }
  return ret;
}

ll my_gcd(ll a, ll b) {
  if (b == 0)
    return a;
  return my_gcd(b, a % b);
}

ll nCk(ll n, ll k) {
  ll kfac = 1, ret = 1;
  for (int i = 1; i <= k; i++) {
    kfac = (kfac * i) % MOD;
  }
  for (int i = n; i >= n - k + 1; i--) {
    ret = (ret * i) % MOD;
  }
  ret = (ret * inv(kfac)) % MOD;
  return ret;
}

void prime_list(int n, vector<int> &primes, vector<bool> &is_prime) {
  int p = 0;
  rep(i, n + 1) is_prime[i] = true;
  is_prime[0] = false;
  is_prime[1] = false;
  for (int i = 2; i <= n; i++) {
    if (is_prime[i]) {
      primes.push_back(i);
      for (int j = 2 * i; j <= n; j += i)
        is_prime[j] = false;
    }
  }
}

ll my_abs(ll a) {
  if (a >= 0)
    return a;
  else
    return -1 * a;
}

Unionfind::Unionfind() {
  par.resize(MAX_N);
  siz.resize(MAX_N);
  rank.resize(MAX_N);
  rep(i, MAX_N) {
    par[i] = i;
    siz[i] = 1;
    rank[i] = 0;
  }
}
ll Unionfind::root(ll x) {
  if (par[x] == x)
    return x;
  else {
    return par[x] = root(par[x]);
  }
}
void Unionfind::merge(ll x, ll y) {
  x = root(x);
  y = root(y);
  if (x == y)
    return;
  if (rank[x] < rank[y]) {
    par[x] = y;
    siz[y] += siz[x];
  } else {
    par[y] = x;
    siz[x] += siz[y];
    if (rank[x] == rank[y])
      rank[x]++;
  }
}
bool Unionfind::issame(ll x, ll y) { return root(x) == root(y); }
ll Unionfind::size(ll x) { return siz[root(x)]; }