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 <iostream>
#include <cstring>
#include <cmath>
#include <queue>
#include <cstdio>
#include <algorithm>
#include <vector>
#define LL long long
#define rg register
using namespace std;
const LL MAXN=1000000LL;
LL N,p,tot,ans=1LL;
LL jl[MAXN],num[MAXN];

template<typename T>inline void in(T &a){
	T ch=getchar(),p=1;
	for(a=0;!isdigit(ch);ch=getchar()) if(ch=='-') p=-1;
	for(;isdigit(ch);ch=getchar()) a=a*10+ch-'0';
	a*=p;
}

template<typename T>inline void print(T x){
	if(x<0) putchar('-'),x=-x;
	if(x>9) print(x/10);
	putchar(x%10+'0');
}

inline LL calc(LL a,LL b){
	LL ans=1LL,base=a;
	while(b){
		if(b%2) ans*=base;
		base*=base;
		b/=2LL; 
	}
	return ans;
}

signed main(){
//	freopen(".in","r",stdin);
//	freopen(".out","w",stdout);
	in(N),in(p);

	if(N==1LL){
		print(p),puts("");
		return 0;
	}

	for(rg LL i=2LL;i<=sqrt(p);i++){
		if((p%i)!=0) continue;
		jl[++tot]=i;
		while((p%i)==0) num[i]++,p/=i;
		if(p==1LL) break;
	}
	
	for(rg int i=1;i<=tot;i++){
		if(num[jl[i]]>=N)
			ans*=calc(jl[i],num[jl[i]]/N);
	}
	
	print(ans),puts("");
	
	fclose(stdin);
	fclose(stdout);
	return 0;
}
/*
1 111

3 24

1000000000000 1000000000000
*/