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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
fscanf(STDIN,"%d %d",$N,$P);

$last=floor(pow($P, 1/$N));

//echo 'last='.$last."\n";

$x=0;$pw=0;
for ($i=$last;$i>0;$i--){
 $ptest=$P;
for ($j=1;$j<=$N;$j++){
  $q=$ptest%$i;
if ($q!=0) break;
  else{
    $pw=$j;
    if ($j<$N) $ptest=$ptest/$i;
//echo $ptest.':'.$pw.':'.$i."\n";
  }
 }
if ($pw==$N) break;
}

echo $i."\n";