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: Accepted)

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll INF = 1e16;
const ll mod = 1000000007;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

int main() {
  ll n, p;
  cin >> n >> p;
  map <ll, ll> s;
  for (ll i = 2; i*i <= p; i++) {
    if (p%i == 0) {
      s[i] = 0;
      while (p%i == 0) {
        s.at(i)++;
        p /= i;
      }
    }
  }
  if (p > 1) s[p] = 1;
  ll res = 1;
  for (auto i : s) {
    res *= (ll)pow(i.first, i.second/n);
  }
  cout << res << endl;
}