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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <utility>
#include <numeric>
#include <cmath>
using namespace std;
//変数デバッグ
#define DEB(variable) cout << #variable << '=' << variable << endl

//for簡易表記(引数ミス防止)
#define FOR(LoopVariable,numberOFbegin,numberOFend) for (int LoopVariable = (numberOFbegin); (LoopVariable) < (numberOFend); (LoopVariable)++)
#define REP(LoopVariable,numberOFend) for(int LoopVariable = 0;(LoopVariable)<(numberOFend);LoopVariable++)


int main(){

    long long int n,p;
    cin>>n>>p;
    long long int max = pow(p, 1 / (n * 1.0));
    long long int i;
    for (i = max; p % ((long long int)pow(i,n)) != 0; i--);
    cout << i << endl;
    return 0;
}