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: Wrong Answer)

<?php
list($n,$p)=explode(" ",trim(fgets(STDIN)));
if($n==1){
echo $p;
}elseif($p==1){
echo 1;
}else{
$ans=1;
$i=2;
while(pow($i,$n)<$p){
$c=pow($i,$n);
if($p%$c==0){
$p/=$c;
$ans*=$i;
--$i;
}
++$i;
}
echo $ans;
}