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: Runtime Error)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
static bool[] isPrimes = makePrimeList(100000);//i-1が素数かどうか

	static void Main()
	{
    string[] input = Console.ReadLine().Split(' ');
    long n = long.Parse(input[0]);
    long p = long.Parse(input[1]);
    long answer = 1;
    long memoNum = 0;
    long memoCount = 0;
    List<long> answers = Factoring(p);
    for(int i = 0; i < answers.Count(); i++)
    {
      //Console.WriteLine(answers[i]);
      if(memoNum == answers[i])
      {
        memoCount++;
        if(memoCount == n)
        {
          answer *= memoNum;
          memoCount = 0;
        }
      }else
      {
        memoNum = answers[i];
        memoCount = 1;
        if(memoCount == n)
        {
          answer *= memoNum;
          memoCount = 0;
        }
      }    
    }
    
		Console.WriteLine(answer);
	}

  static List<long> Factoring(long originalNum)//引数をO(√n)で素因数分解。リストには同じ数も含む。
  {
    List<long> answers = new List<long>();
    for(long i = 2; i <= Math.Sqrt(originalNum); i++)
    {
      if(!isPrimes[i-1]) continue;//素数でないとき
      else
      {
        while(originalNum % i == 0)
        {
          originalNum /= i;
          answers.Add(i);
        }
      }
    }
    if(originalNum != 1) answers.Add(originalNum);
    return answers;
  }

  static bool[] makePrimeList(long maxPrime)//「引数1以上」max以下の素数判定。エラトステネスの篩を用いる。
  {
    bool[] isPrimes = new bool[maxPrime];//素数リスト
    isPrimes[0] = false;//1は素数でないのでfalse
    for(long i = 1; i < maxPrime; i++) isPrimes[i] = true;//素数と仮定してtrue
    
    for(long i = 2; i <= Math.Sqrt(maxPrime); i++)
    {
      if(isPrimes[i-1])
      {
        for (long j = i*2; j <= maxPrime; j+=i)
        {
          isPrimes[j-1] = false;//素数でないのでfalse
        }
      }
    }

    return isPrimes;
  }
  
}