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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

typedef long long int LL;
#define REP(n) for(LL i = 0; i < (n); i++)
#define COUT(val) cout << (val) << endl
#define CIN(val) cin >> (val)
#define SORT(vec) sort(vec.begin(), vec.end())
#define SORT_GRE(vec) sort(vec.begin(), vec.end(), greater<LL>())

int main(){
    LL n, p;
    cin >> n >> p;
    LL powNum, keeper;
    for(LL i = 1; i <= 1145141919; i++){
        powNum = pow(i, n);
        if(powNum > p){
            powNum = pow(i-1, n);
            keeper = i - 1;
            break;
        } else if(powNum == p){
            cout << i << endl;
            return 0;
        }
    }
    while(1){
        if(p % powNum == 0){
            cout << keeper << endl;
            return 0;
        } else {
            keeper--;
            powNum = pow(keeper, n);
        }
    }
    return 0;
}