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>
#define REP(i, a, n) for (ll i = ((ll) a); i < ((ll) n); i++)
using namespace std;
typedef long long ll;

int main(void) {
  ll N, P;
  cin >> N >> P;

  vector<bool> isp(2000000, true);
  isp[0] = isp[1] = false;
  REP(i, 0, 2000000) {
    if (isp[i]) {
      for (ll j = i * 2; j < 2000000; j += i) {
        isp[j] = false;
      }
    }
  }
  vector<ll> p;
  REP(i, 0, 2000000) if (isp[i]) p.push_back(i);

  ll ans = 1;
  ll x = P;
  REP(i, 0, p.size()) {
    ll cnt = 0;
    while (x % p[i] == 0) {
      x /= p[i];
      cnt++;
    }
    REP(j, 0, cnt / N) {
      ans *= p[i];
    }
  }
  if (N == 1) {
    ans *= x;
  }
  cout << ans << endl;
}