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;
using static Atcoder;
using System.Threading.Tasks;
using System.ComponentModel;

public class Hello
{
    public static void Main()
    {
        long[] NP = LSRead();
        long N = NP[0], P = NP[1];
        if (P == 1) { Console.WriteLine(1); return; }
        if(N == 1) { Console.WriteLine(P); return; }
        var primeFactor = new PrimeFactor();
        var factors = primeFactor.Enumerate(P);
        Dictionary<long, long> dic = new Dictionary<long, long>();
        foreach (var l in factors)
        {
            if (!dic.ContainsKey(l)) dic[l] = 1;
            else dic[l]++;
        }
        var sorted = dic.OrderByDescending(v => v.Key);
        long ans = 1;
        foreach (var v in sorted) {
            if (v.Value >= N) {
                ans *= (long)Math.Pow(v.Key,v.Value/N);
            }
        }
        Console.WriteLine(ans);

    }
}

public class PrimeFactor
{

    public IEnumerable<long> Enumerate(long n)
    {
        while (n > 1)
        {
            long factor = GetFactor(n);
            yield return factor;
            n = n / factor;
        }
    }

    private long GetFactor(long n, int seed = 1)
    {
        if (n % 2 == 0)
            return 2;
        if (IsPrime(n))
            return n;
        long x = 2;
        long y = 2;
        long d = 1;
        long count = 0;
        while (d == 1)
        {
            count++;
            x = f(x, n, seed);
            y = f(f(y, n, seed), n, seed);
            d = Gcd(Math.Abs(x - y), n);
        }
        if (d == n)
            // 見つからなかった、乱数発生のシードを変えて再挑戦。
            return GetFactor(n, seed + 1);
        // 素数でない可能性もあるので、再度呼び出す
        return GetFactor(d);
    }

    private int[] seeds = new int[] { 3, 5, 7, 11, 13, 17 };
    private long f(long x, long n, int seed)
    {
        return (seeds[seed % 6] * x + seed) % n;
    }

    private static long Gcd(long a, long b)
    {
        if (a < b)
            return Gcd(b, a);  // 引数を入替えて自分を呼び出す
        if (b == 0)
            return a;
        long d = 0;
        do
        {
            d = a % b;
            a = b;
            b = d;
        } while (d != 0);
        return a;
    }

    // 効率は良くないが、これでも十分な速度がでたので、良しとする。
    private static bool IsPrime(long number)
    {
        long boundary = (long)Math.Floor(Math.Sqrt(number));

        if (number == 1)
            return false;
        if (number == 2)
            return true;

        for (long i = 2; i <= boundary; ++i)
        {
            if (number % i == 0)
                return false;
        }

        return true;
    }
}


public class Atcoder
{
    static void Swap<T>(ref T a, ref T b)
    {
        var t = a;
        a = b;
        b = t;
    }
    public static int LCM(int a, int b)
    {
        int c = a * b;
        if (a < b) Swap(ref a, ref b);
        int d = a % b;
        while (d != 0)
        {
            a = b;
            b = d;
            d = a % b;
        }
        return c / b;
    }
    public static string StrReverce(string s)
    {
        return new string(s.Reverse().ToArray());
    }
    public static int intRead()
    {
        return int.Parse(Console.ReadLine());
    }
    public static bool IsPrime(int n)
    {
        if (n < 2) return false;
        if (n == 2) return true;
        if (n % 2 == 0) return false;

        //double sqrtNum = Math.Sqrt(n);
        for (int i = 3; i < n; i += 2)
        {
            if (n % i == 0) return false;
        }
        return true;
    }
    public static string[] SpRead(char c)
    {
        return Console.ReadLine().Split(c);
    }
    public static long[] LSRead()
    {
        return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
    }
}