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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

#!/usr/bin/perl

use strict;
use warnings;
use 5.010;

use Data::Dumper;
use POSIX qw(floor);

my @INPUT;
while (<>) {
    chomp;
    push @INPUT, $_;
}

my ($N, $P) = split " ", shift @INPUT;

my $n = $P;
my @f = factorization($n);
my %f;
for my $f (@f) {
    $f{$f}++;
}

my $ans = 1;

for my $d (keys %f) {
    my $num = $f{$d};
    my $times = floor($num / $N);
    $ans = $ans * ($d ** $times);
}

say $ans;

sub factorization {
    my $n = shift;
    my @f;
    for my $i (2 .. ($n - 1)) {
        while ($n % $i == 0) {
            $n = $n / $i;
            push @f, $i;
        }
        if ($n == 1) {
            last;
        }
    }
    return @f;
}