Problem p03196 (C++)

Buggy submission (status: Time Limit Exceeded):
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const int INF = 1e9;
const ll LINF = 1e18;
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class S, class T>
ostream &operator<<(ostream &out, const pair<S, T> &o) {
  out << "(" << o.first << "," << o.second << ")";
  return out;
}
template <class T> ostream &operator<<(ostream &out, const vector<T> V) {
  for (int i = 0; i < V.size(); i++) {
    out << V[i];
    if (i != V.size() - 1)
      out << " ";
  }
  return out;
}
template <class T>
ostream &operator<<(ostream &out, const vector<vector<T>> Mat) {
  for (int i = 0; i < Mat.size(); i++) {
    if (i != 0)
      out << endl;
    out << Mat[i];
  }
  return out;
}
template <class S, class T>
ostream &operator<<(ostream &out, const map<S, T> mp) {
  out << "{ ";
  for (auto it = mp.begin(); it != mp.end(); it++) {
    out << it->first << ":" << it->second;
    if (mp.size() - 1 != distance(mp.begin(), it))
      out << ", ";
  }
  out << " }";
  return out;
}

/*
 <url:>
 問題文============================================================
 =================================================================
 解説=============================================================
 ================================================================
 */

/* 素因数分解 */
void PrimeFact(ll n, map<ll, ll> &mp) {
  while (n != 1) {
    if (n == 2 || n == 3) {
      mp[n]++;
      n /= n;
      continue;
    }
    bool prime_flag = false;
    for (int i = 2; i * i <= n; i++) {
      if (n % i == 0) {
        mp[i]++;
        n /= i;
        prime_flag = true;
        break;
      }
    }
    if (!prime_flag) {
      mp[n]++;
      n /= n;
    }
  }
}

const ll MOD = LLONG_MAX;
ll powmod(ll a, ll b) {
  ll res = 1;
  a %= MOD;
  for (; b; b >>= 1) {
    if (b & 1)
      res = res * a % MOD;
    a = a * a % MOD;
  }
  return res;
}

template <class Type> Type solve(Type res = Type()) {
  ll N, P;
  cin >> N >> P;
  map<ll, ll> mp;
  PrimeFact(P, mp);
  res = 1;
  for (auto p : mp) {
    if (p.second >= N) {
      res *= powmod(p.first, p.second / N);
    }
  }
  return res;
}
int main(void) {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  // solve(0);
  cout << fixed << setprecision(15) << solve<ll>() << endl;
  return 0;
}


Fixed submission:
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const int INF = 1e9;
const ll LINF = 1e18;
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class S, class T>
ostream &operator<<(ostream &out, const pair<S, T> &o) {
  out << "(" << o.first << "," << o.second << ")";
  return out;
}
template <class T> ostream &operator<<(ostream &out, const vector<T> V) {
  for (int i = 0; i < V.size(); i++) {
    out << V[i];
    if (i != V.size() - 1)
      out << " ";
  }
  return out;
}
template <class T>
ostream &operator<<(ostream &out, const vector<vector<T>> Mat) {
  for (int i = 0; i < Mat.size(); i++) {
    if (i != 0)
      out << endl;
    out << Mat[i];
  }
  return out;
}
template <class S, class T>
ostream &operator<<(ostream &out, const map<S, T> mp) {
  out << "{ ";
  for (auto it = mp.begin(); it != mp.end(); it++) {
    out << it->first << ":" << it->second;
    if (mp.size() - 1 != distance(mp.begin(), it))
      out << ", ";
  }
  out << " }";
  return out;
}

/*
 <url:>
 問題文============================================================
 =================================================================
 解説=============================================================
 ================================================================
 */

/* 素因数分解 */
void PrimeFact(ll n, map<ll, ll> &mp) {
  while (n != 1) {
    if (n == 2 || n == 3) {
      mp[n]++;
      n /= n;
      continue;
    }
    bool prime_flag = false;
    for (ll i = 2; i * i <= n; i++) {
      if (n % i == 0) {
        mp[i]++;
        n /= i;
        prime_flag = true;
        break;
      }
    }
    if (!prime_flag) {
      mp[n]++;
      n /= n;
    }
  }
}

const ll MOD = LLONG_MAX;
ll powmod(ll a, ll b) {
  ll res = 1;
  a %= MOD;
  for (; b; b >>= 1) {
    if (b & 1)
      res = res * a % MOD;
    a = a * a % MOD;
  }
  return res;
}

template <class Type> Type solve(Type res = Type()) {
  ll N, P;
  cin >> N >> P;
  map<ll, ll> mp;
  PrimeFact(P, mp);
  res = 1;
  for (auto p : mp) {
    if (p.second >= N) {
      res *= powmod(p.first, p.second / N);
    }
  }
  return res;
}
int main(void) {
  cin.tie(0);
  ios_base::sync_with_stdio(false);
  // solve(0);
  cout << fixed << setprecision(15) << solve<ll>() << endl;
  return 0;
}