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: Wrong Answer)

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

public static class Prime
{
    public static bool IsPrime(int n)
    {
        return GetPrimes(n).Last() == n;
    }

    // Sieve of Eratosthenes
    public static int[] GetPrimes(int n)
    {
        var sieve = new BitArray(n + 1);
        var end = (int)(Math.Sqrt(n) + 0.1);
        for (int i = 2; i <= end; i++)
        {
            if (!sieve.Get(i))
            {
                for (int j = i * 2; j <= n; j += i)
                {
                    sieve.Set(j, true);
                }
            }
        }

        return Enumerable.Range(2, n - 1).Where(i => !sieve.Get(i)).ToArray();
    }

    public static List<long> PrimeFactorize(long n, IEnumerable<long> primes)
    {
        var factor = new List<long>();
        while (n > 1)
        {
            foreach (var p in primes)
            {
                if (n % p == 0)
                {
                    factor.Add(p);
                    n /= p;
                    break;
                }
            }
        }
        return factor;
    }

    // 要素を各個数で表す
    public static Dictionary<long, int> FactorToDict(IEnumerable<long> factor)
    {
        var dict = new Dictionary<long, int>();

        foreach (var f in factor)
        {
            if (!dict.ContainsKey(f))
            {
                dict[f] = 0;
            }
            dict[f]++;
        }

        return dict;
    }
}

class Solution
{
    static void Main()
    {
        var vals = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        var n = vals[0];
        var p = vals[1];

        var primeTmps = Prime.GetPrimes((int)(Math.Sqrt(p) + 1));
        var primes = new HashSet<long>();
        foreach (var pr0 in primeTmps)
        {
            var prs = new long[] { (long)pr0, p / pr0 };
            foreach (var pr in prs)
            {
                if (!primes.Contains(pr))
                {
                    primes.Add(pr);
                }
            }
        }
        var factors = Prime.FactorToDict(Prime.PrimeFactorize(p, primes));

        var gcd = 1L;
        foreach (var f in factors)
        {
            var count = f.Value / n;
            if (count > 0)
            {
                gcd *= (long)Math.Pow(f.Key, count);
            }
        }

        Console.WriteLine(gcd);
    }
}