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;
#define rep(i, n) for (int i = 0; i < n; i++)
typedef long long ll;
int main()
{
  ll N, P;
  cin >> N >> P;
  if (N == 1)
  {
    cout << P << endl;
    return 0;
  }
  if (N > sqrt(P))
  {
    cout << 1 << endl;
    return 0;
  }
  ll ans = 1;
  for (int i = 2; i <= sqrt(P) + 2; i++)
  {
    int cnt = 0;
    while (P % i == 0)
    {
      P /= i;
      cnt++;
      if (cnt == N)
      {
        ans *= i;
        cnt = 0;
      }
    }
  }
  cout << ans << endl;
  return 0;
}