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;

class Program {
    static void Main(string[] args) {
        //入力
        string s = Console.ReadLine();
        string[] t = s.Split(' ');

        //変数の割り当て
        int N = int.Parse(t[0]);
        int P = int.Parse(t[1]);

        //回答となる数字
        int ans = 1;

        //PのN乗根まで、割り切れる最大の値をチェックする
        for (int i = 1; i <= P; i++) {
            //iのN乗でPを割り切れるか判定
            if (P % (Math.Pow(i, N)) == 0) {
                ans = i;
            }

            //iのN乗がPを超えたら終了
            if (Math.Pow(i, N) > P) {
                break;
            }
        }

        //出力
        Console.WriteLine(ans);
    }
}