Problem:
Score : 300 points

Problem Statement

There are N integers a_1, a_2, ..., a_N not less than 1.
The values of a_1, a_2, ..., a_N are not known, but it is known that a_1 \times a_2 \times ... \times a_N = P.

Find the maximum possible greatest common divisor of a_1, a_2, ..., a_N.

Constraints

1 \leq N \leq 10^{12}

1 \leq P \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N P

Output

Print the answer.

Sample Input 1

3 24

Sample Output 1

2

The greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.

Sample Input 2

5 1

Sample Output 2

1

As a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.

Sample Input 3

1 111

Sample Output 3

111

Sample Input 4

4 972439611840

Sample Output 4

206

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define FOR(i, a, b) for(int i=(a); i<(b); i++)
#define REP(i, n) FOR(i, 0, n)
#define all(x) (x).begin(), (x).end()
#define bit(x) (1L << (x))
using ll = long long;
using namespace std;

ll m_pow(ll x, ll n){
  if(n == 0) return 1;
  return m_pow(x*x, n/2) * ((n%2)?x: 1);
}

int main(){
  ll n, p; cin >> n >> p;

  ll ans = 1;

  vector<pair<ll, ll>> v;
  for(ll i=2; p>=i*i; i++){
    ll cnt = 0;
    while(p % i == 0){
      p /= i;
      cnt++;
    }
    v.push_back({i, cnt});
  }

  for(const auto& x: v){
    ans *= m_pow(x.first, x.second / n);
  }
  
  cout << ans << endl;

  return 0;
}