Problem p03253 (C++)

Buggy submission (status: Runtime Error):
// header
#ifdef LOCAL
#include "/Users/takakurashokichi/Desktop/atcoder/cxx-prettyprint-master/prettyprint.hpp"
#define debug(x) cout << x << endl
#else
#define debug(...) 42
#endif
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
// types
using namespace std;
using ll = long long;
using ul = unsigned long long;
using ld = long double;
typedef pair<ll, ll> Pl;
typedef pair<int, int> Pi;
typedef vector<ll> vl;
typedef vector<int> vi;
template <typename T> using mat = vector<vector<T>>;
template <int mod> struct modint {
  int x;

  modint() : x(0) {}

  modint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  modint &operator+=(const modint &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  modint &operator-=(const modint &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  modint &operator*=(const modint &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  modint &operator/=(const modint &p) {
    *this *= p.inverse();
    return *this;
  }

  modint operator-() const { return modint(-x); }

  modint operator+(const modint &p) const { return modint(*this) += p; }

  modint operator-(const modint &p) const { return modint(*this) -= p; }

  modint operator*(const modint &p) const { return modint(*this) *= p; }

  modint operator/(const modint &p) const { return modint(*this) /= p; }

  bool operator==(const modint &p) const { return x == p.x; }

  bool operator!=(const modint &p) const { return x != p.x; }

  modint inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return modint(u);
  }

  modint pow(int64_t n) const {
    modint ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const modint &p) { return os << p.x; }

  friend istream &operator>>(istream &is, modint &a) {
    int64_t t;
    is >> t;
    a = modint<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};
// abreviations
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep_(i, a_, b_, a, b, ...)                                             \
  for (int i = (a), max_i = (b); i < max_i; i++)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define rrep_(i, a_, b_, a, b, ...)                                            \
  for (int i = (b - 1), min_i = (a); i >= min_i; i--)
#define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define SZ(x) ((int)(x).size())
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp make_pair
#define print(x) cout << x << endl
#define vsum(x) accumulate(all(x), 0LL)
#define vmax(a) *max_element(all(a))
#define vmin(a) *min_element(all(a))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
// functions
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T> T mypow(T x, ll n) {
  T ret = 1;
  while (n > 0) {
    if (n & 1)
      (ret *= x);
    (x *= x);
    n >>= 1;
  }
  return ret;
}
ll modpow(ll x, ll n, const ll mod) {
  ll ret = 1;
  while (n > 0) {
    if (n & 1)
      (ret *= x);
    (x *= x);
    n >>= 1;
    x %= mod;
    ret %= mod;
  }
  return ret;
}
uint64_t my_rand(void) {
  static uint64_t x = 88172645463325252ULL;
  x = x ^ (x << 13);
  x = x ^ (x >> 7);
  return x = x ^ (x << 17);
}
// graph template
template <typename T> struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }
  operator int() const { return to; }
};
template <typename T> using Edges = vector<edge<T>>;
template <typename T> using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;

// constant
// #define inf 1000000005LL
#define inf 4000000000000000005LL
#define mod 1000000007LL
#define endl '\n'
typedef modint<mod> mint;
const long double eps = 0.0001;
const long double PI = 3.141592653589793;
// library
bool is_prime(ll n) {
  if (n <= 1)
    return false;
  if (n == 2)
    return true;
  if (n % 2 == 0)
    return false;
  ll d = n - 1;
  while (d % 2 == 0)
    d /= 2;
  vl primes;
  if (n < 4759123140)
    primes = {2, 7, 61};
  else
    primes = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
  for (ll a : primes) {
    a %= n;
    if (a == 0)
      return true;
    ll t = d;
    ll y = modpow(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = __int128_t(y) * y % n;
      // y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  return true;
}
// MR is necessary
// In codeforces, delete __int128 in the second line.
// about O(N^1/4logN)
ll pollard_single(ll n) {
  auto f = [&](ll x) { return (__int128_t(x) * x + 1) % n; };
  // auto f = [&](ll x) { return (x * x + 1) % n; };
  if (is_prime(n))
    return n;
  if (n % 2 == 0)
    return 2;
  ll st = 0;
  while (true) {
    st = my_rand() % n;
    ll x = st, y = f(x);
    while (true) {
      ll p = gcd((y - x + n), n);
      if (p == 0 || p == n)
        break;
      if (p != 1)
        return p;
      x = f(x);
      y = f(f(y));
    }
  }
}

vl pollard_rec(ll n) {
  if (n == 1)
    return {};
  ll x = pollard_single(n);
  if (x == n)
    return {x};
  vl a = pollard_rec(x);
  vl b = pollard_rec(n / x);
  a.insert(a.end(), b.begin(), b.end());
  return a;
}

map<ll, int> pollard(ll n) {
  map<ll, int> res;
  for (ll a : pollard_rec(n)) {
    res[a]++;
  }
  return res;
}
template <typename T> struct Combination {
  vector<T> _fact, _rfact, _inv;

  Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for (int i = 1; i <= sz; i++)
      _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for (int i = sz - 1; i >= 0; i--)
      _rfact[i] = _rfact[i + 1] * (i + 1);
    for (int i = 1; i <= sz; i++)
      _inv[i] = _rfact[i] * _fact[i - 1];
  }

  inline T fact(int k) const { return _fact[k]; }

  inline T rfact(int k) const { return _rfact[k]; }

  inline T inv(int k) const { return _inv[k]; }

  T P(int n, int r) const {
    if (r < 0 || n < r)
      return 0;
    return fact(n) * rfact(n - r);
  }

  T C(int p, int q) const {
    if (q < 0 || p < q)
      return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }

  T H(int n, int r) const {
    if (n < 0 || r < 0)
      return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
int main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << setprecision(20);
  Combination<mint> comb(1000);
  ll n, m;
  cin >> n >> m;
  auto res = pollard(m);
  mint ans = 1;
  for (auto p : res) {
    ans *= comb.C(p.second + n - 1, n - 1);
  }
  print(ans);
}

Fixed submission:
// header
#ifdef LOCAL
#include "/Users/takakurashokichi/Desktop/atcoder/cxx-prettyprint-master/prettyprint.hpp"
#define debug(x) cout << x << endl
#else
#define debug(...) 42
#endif
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
// types
using namespace std;
using ll = long long;
using ul = unsigned long long;
using ld = long double;
typedef pair<ll, ll> Pl;
typedef pair<int, int> Pi;
typedef vector<ll> vl;
typedef vector<int> vi;
template <typename T> using mat = vector<vector<T>>;
template <int mod> struct modint {
  int x;

  modint() : x(0) {}

  modint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  modint &operator+=(const modint &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  modint &operator-=(const modint &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  modint &operator*=(const modint &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  modint &operator/=(const modint &p) {
    *this *= p.inverse();
    return *this;
  }

  modint operator-() const { return modint(-x); }

  modint operator+(const modint &p) const { return modint(*this) += p; }

  modint operator-(const modint &p) const { return modint(*this) -= p; }

  modint operator*(const modint &p) const { return modint(*this) *= p; }

  modint operator/(const modint &p) const { return modint(*this) /= p; }

  bool operator==(const modint &p) const { return x == p.x; }

  bool operator!=(const modint &p) const { return x != p.x; }

  modint inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return modint(u);
  }

  modint pow(int64_t n) const {
    modint ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const modint &p) { return os << p.x; }

  friend istream &operator>>(istream &is, modint &a) {
    int64_t t;
    is >> t;
    a = modint<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};
// abreviations
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep_(i, a_, b_, a, b, ...)                                             \
  for (int i = (a), max_i = (b); i < max_i; i++)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define rrep_(i, a_, b_, a, b, ...)                                            \
  for (int i = (b - 1), min_i = (a); i >= min_i; i--)
#define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define SZ(x) ((int)(x).size())
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp make_pair
#define print(x) cout << x << endl
#define vsum(x) accumulate(all(x), 0LL)
#define vmax(a) *max_element(all(a))
#define vmin(a) *min_element(all(a))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
// functions
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T> T mypow(T x, ll n) {
  T ret = 1;
  while (n > 0) {
    if (n & 1)
      (ret *= x);
    (x *= x);
    n >>= 1;
  }
  return ret;
}
ll modpow(ll x, ll n, const ll mod) {
  ll ret = 1;
  while (n > 0) {
    if (n & 1)
      (ret *= x);
    (x *= x);
    n >>= 1;
    x %= mod;
    ret %= mod;
  }
  return ret;
}
uint64_t my_rand(void) {
  static uint64_t x = 88172645463325252ULL;
  x = x ^ (x << 13);
  x = x ^ (x >> 7);
  return x = x ^ (x << 17);
}
// graph template
template <typename T> struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }
  operator int() const { return to; }
};
template <typename T> using Edges = vector<edge<T>>;
template <typename T> using WeightedGraph = vector<Edges<T>>;
using UnWeightedGraph = vector<vector<int>>;

// constant
// #define inf 1000000005LL
#define inf 4000000000000000005LL
#define mod 1000000007LL
#define endl '\n'
typedef modint<mod> mint;
const long double eps = 0.0001;
const long double PI = 3.141592653589793;
// library
bool is_prime(ll n) {
  if (n <= 1)
    return false;
  if (n == 2)
    return true;
  if (n % 2 == 0)
    return false;
  ll d = n - 1;
  while (d % 2 == 0)
    d /= 2;
  vl primes;
  if (n < 4759123140)
    primes = {2, 7, 61};
  else
    primes = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
  for (ll a : primes) {
    a %= n;
    if (a == 0)
      return true;
    ll t = d;
    ll y = modpow(a, t, n);
    while (t != n - 1 && y != 1 && y != n - 1) {
      y = __int128_t(y) * y % n;
      // y = y * y % n;
      t <<= 1;
    }
    if (y != n - 1 && t % 2 == 0) {
      return false;
    }
  }
  return true;
}
// MR is necessary
// In codeforces, delete __int128 in the second line.
// about O(N^1/4logN)
ll pollard_single(ll n) {
  auto f = [&](ll x) { return (__int128_t(x) * x + 1) % n; };
  // auto f = [&](ll x) { return (x * x + 1) % n; };
  if (is_prime(n))
    return n;
  if (n % 2 == 0)
    return 2;
  ll st = 0;
  while (true) {
    st = my_rand() % n;
    ll x = st, y = f(x);
    while (true) {
      ll p = gcd((y - x + n), n);
      if (p == 0 || p == n)
        break;
      if (p != 1)
        return p;
      x = f(x);
      y = f(f(y));
    }
  }
}

vl pollard_rec(ll n) {
  if (n == 1)
    return {};
  ll x = pollard_single(n);
  if (x == n)
    return {x};
  vl a = pollard_rec(x);
  vl b = pollard_rec(n / x);
  a.insert(a.end(), b.begin(), b.end());
  return a;
}

map<ll, int> pollard(ll n) {
  map<ll, int> res;
  for (ll a : pollard_rec(n)) {
    res[a]++;
  }
  return res;
}
template <typename T> struct Combination {
  vector<T> _fact, _rfact, _inv;

  Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for (int i = 1; i <= sz; i++)
      _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for (int i = sz - 1; i >= 0; i--)
      _rfact[i] = _rfact[i + 1] * (i + 1);
    for (int i = 1; i <= sz; i++)
      _inv[i] = _rfact[i] * _fact[i - 1];
  }

  inline T fact(int k) const { return _fact[k]; }

  inline T rfact(int k) const { return _rfact[k]; }

  inline T inv(int k) const { return _inv[k]; }

  T P(int n, int r) const {
    if (r < 0 || n < r)
      return 0;
    return fact(n) * rfact(n - r);
  }

  T C(int p, int q) const {
    if (q < 0 || p < q)
      return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }

  T H(int n, int r) const {
    if (n < 0 || r < 0)
      return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
int main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << setprecision(20);
  Combination<mint> comb(200000);
  ll n, m;
  cin >> n >> m;
  auto res = pollard(m);
  mint ans = 1;
  for (auto p : res) {
    ans *= comb.C(p.second + n - 1, n - 1);
  }
  print(ans);
}