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 ll;
typedef long long int llint;
typedef pair<ll, ll> pa;
#define MM 1000000000
#define MOD MM+7
#define MAX 101000
#define MAP 110
#define initial_value -1
#define Pair pair<int,int>
#define chmax(a,b) (a<b ? a=b:0)
#define chmin(a,b) (a>b ? a=b:0)
#define INF (1 << 29) //536870912
int dx[4] = {-1,0,1,0};
int dy[4] = {0,-1,0,1};
ll N,P;
int main(){
    cin >> N >> P;
    map<ll,int> mp;
    ll num = P;
    for(ll i = 2; i <= P; i++){
        while(num % i == 0){
            mp[i]++;
            num /= i;
            // cout << i << " ";
        }
    }
    //cout << endl;
    ll ans = 1;
    for(ll i = 2; i <= P; i++){
        if(mp[i] >= N){
            ans *= i;
        }
    }
    cout << ans << endl;
}