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.Generic;
using System.Linq;

namespace C
{
	class C
	{
		static void Main(string[] args)
		{
			string[] inputs = Console.ReadLine().Split(' ');
			ulong N = ulong.Parse(inputs[0]);
			ulong P = ulong.Parse(inputs[1]);

			Dictionary<ulong, ulong> prime = new Dictionary<ulong, ulong>();
			ulong p = P;
			int x;
			if(p == 1) {
				Console.WriteLine(1);
				return;
			}
			if(N == 1) {
				Console.WriteLine(P);
				return;
			}
			List<ulong> pnum = new List<ulong>();
			for(ulong i=2; i<=Math.Sqrt(P); i++) {
				if(IsPrime(i)) pnum.Add(i);
			}

			for(x=0; x<pnum.Count; x++) {
				for(ulong i=0; (p%pnum[x])==0; i++) {
					if(prime.ContainsKey(pnum[x]))
						prime[pnum[x]]++;
					else prime.Add(pnum[x], 1);
					p /= pnum[x];
				}
			}
			
			var C = prime.Where(n => n.Value >= N).Select(n => n.Key).ToList();
			if(C.Count == 0) {
				Console.WriteLine(1);
				return;
			}
			Console.WriteLine(C.Aggregate((now, next) => now * next));
		}

		public static bool IsPrime(ulong num)
		{
			if(num < 2) return false;
			else if(num == 2) return true;
			else if(num % 2 == 0) return false;

			double sqrtNum = Math.Sqrt(num);
			for(ulong i = 3; i <= sqrtNum; i += 2) {
				if(num % i == 0) {
					return false;
				}
			}
			return true;
		}
	}
}