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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

namespace AtCoder {
    class Program {
        static void Main() {
            long[] input = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
            long n = input[0];
            long p = input[1];
            if(n == 1) { Console.WriteLine(p); return; }
            long pow = 0, pro = 1;
            for(long prime = 2; pow < p; prime++) {
                pow = Pow(prime, n);
                if(pow == -1) break;
                while(p % pow == 0) {
                    p /= pow;
                    pro *= prime;
                }
            }
            Console.WriteLine(pro);
        }
        static long Pow(long a, long n) {
            if(n == 0) return 1;
            if(n == 1) return a;
            long b = Pow(a, n / 2);
            if(b == -1 || b > 1000000) return -1;
            return b * b * Pow(a, n % 2);
        }
    }
}