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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>

using namespace std;
using ll = long long;

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

  ll pos = 2;
  vector<ll> vec;
  ll tmp = p;
  ll cnt = 1;
  ll last = -1;
  while (true) {
    if (tmp == 1 || sqrt(p) < pos) {
      break;
    }
    else if (tmp / pos * pos == tmp) {
      tmp /= pos;
      cnt += last == pos;
      last = pos;
      if (cnt == n) {
        vec.push_back(pos);
        cnt = 0;
      }
    }
    else {
      last = pos;
      ++pos;
      cnt = 1;
    }
  }

  ll ans = 1;
  for (auto &v : vec)
    ans *= v;
  cout << (n != 1 ? ans : p) << endl;
}