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>
using namespace std;
using ll = long long;
using P = pair<int,int>;
using node = pair<string,ll>;
const ll inf = numeric_limits<ll>::max()/3;
const ll mod = 1e9+7;
#define maxPrime 10000000

int prime[maxPrime];

int main(void) {
  ll n,p;
  cin >> n >> p;
  if(n == 1) {
    cout << p << endl;
  }
  vector< ll > primes;
  fill(prime, prime + maxPrime, 1);
  for(ll i = 2;i < maxPrime;++i){
    if(prime[i]){
      primes.push_back(i);
      for(ll j = i*2;j < maxPrime;j += i){
        prime[j] = 0;
      }
    }
  }
  ll res = 1;
  for(ll i : primes) {
    ll cnt = 0;
    ll d = (ll)pow(i,n);
    while(p % d == 0) {
      p /= d;
      res *= i;
    }
  }
  cout << res << endl;
}