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 <cstdio>
#include <iostream>
#include <string>
#include <algorithm>
#include <cstring>
#include <utility>
#include <vector>
#include <map>
#include <set>
#include <cmath>
#include <queue>
#include <bitset>
#include <stack>
#include <deque>
using namespace std;
typedef pair<int, int> pii;
typedef long long LL;

int main() {
    LL N, M;
    scanf("%lld %lld", &N, &M);
    if (N == 1) return !printf("%lld\n", M);
    LL sq = (LL)sqrt(M);
    LL ans = 1;
    for (int i = 2; i <= sq; i++) {
        int cnt = 0;
        while (M % i == 0) {
              cnt++;
              M /= i;
        }
        ans *= (pow(i, cnt / N));
    }
    printf("%lld\n", ans);
    return 0;
}