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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner();
		long n = sc.nextLong();
		long p = sc.nextLong();

		long max = 1;
		long x;
		for(long i = 1;(x = (long)Math.pow(i, n)) <= p; i++){
			if(p % x == 0 && max < x)
				max = i;

			long r = p+1 - i;
			long pow = (long)Math.pow(r,n);
			if(p % r == 0 && pow <= p){
				max = r;
				break;
			}
		}

		System.out.println(max);
	}
}

class Scanner {
	private static final int SPACE = (int)' ';
	private static final int LINE_END_0 = 13;
	private static final int LINE_END_1 = 10;
	private static final int BEFORE = -1;
	private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	
	public String next(){
		StringBuilder sb = new StringBuilder();
		
		int length = BEFORE;
		readLoop: while(true) {
			try {
				int value = br.read();
				switch(value) {
				case LINE_END_1:
					if(length == BEFORE)
						break;
					
					if((int)sb.charAt(length) == LINE_END_0)
						sb.deleteCharAt(length);
				case SPACE:
					break readLoop;
				}
				sb.append((char)value);
				length++;

			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}
		return sb.toString();
	}
	
	public String[] nextArray(int length) {
		String[] array = new String[length];
		for(int i = 0; i < length; i++)
			array[i] = next();
		return array;
	}
	
	public double nextDouble() {
		return Double.parseDouble(next());
	}
	
	public double[] nextDoubleArray(int length) {
		double[] array = new double[length];
		for(int i = 0; i < length; i++)
			array[i] = nextDouble();
		return array;
	}
	
	public int nextInt() {
		return Integer.parseInt(next());
	}
	
	public int[] nextIntArray(int length) {
		int[] array = new int[length];
		for(int i = 0; i < length; i++)
			array[i] = nextInt();
		return array;
	}
	
	public long nextLong() {
		return Long.parseLong(next());
	}
	
	public long[] nextLongArray(int length) {
		long[] array = new long[length];
		for(int i = 0; i < length; i++)
			array[i] = nextLong();
		return array;
	}
	
	public boolean ready() {
		try {
			return br.ready();
		} catch (IOException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
		return false;
	}
}