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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
$input = explode(' ', trim(fgets(STDIN)));
$n = (int)$input[0];
$p = (int)$input[1];

$max = floor(sqrt($p));
$as = [];

if ($n === 1) {
	echo $p;
	exit();
}
for ($i=2; $i <= $max; $i++) { 
	while ( $p % $i === 0) {
		if (empty($as[$i])) {
			$as[$i] = 1;
		}else{
			$as[$i] += 1;
		}
		$p = floor($p/$i);
	}
}
$min = 1;
foreach ($as as $key => $value) {
	if ($value >= $n) {
		$jo = floor($value / $n);
		$min *= pow($key, $jo);
	}
}
echo $min;