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: Runtime Error)

#include<bits/stdc++.h>
#define start_routine cin.tie(0); cout.tie(0); ios_base::sync_with_stdio(false); int begtime = clock();
#define end_routine int endtime = clock(); cerr << endl << "Time elapsed: " << (endtime - begtime)*1000/CLOCKS_PER_SEC << " ms"; return 0;
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define int long long
#define mp make_pair
#define fr(i,a,b) for(i=a;i<b;i++)
#define mod 1000000007
#define FILEIO freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout);
using namespace std;

vector <int> v;
bool b[1000000] = {0};
void calculate()
{
	int i;
	fr(i,2,1000001)
	{
		if(b[i] == 0)
		{
			v.pb(i);
			int j;
			for(j = i*i; j<=1000000; j+=i) b[j] = 1;
		}
	}
}
signed main()
{
	//FILEIO
 	//start_routine
	
	calculate();
	int n,p;
	cin>>n>>p;

	int ans = 1;
	int i;
	fr(i,0,v.size())
	{
		if(p%v[i] == 0)
		{
			int temp =0;
			while(p%v[i] == 0)
			{
				temp++;
				p/=v[i];
			}
			int t = temp/n;
			while(t--)
			{
				ans *= v[i];
			}
		}
	}

	cout<<ans<<'\n';

 	//end_routine
}