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: Time Limit Exceeded)

<?php
ini_set('memory_limit', '1024M');
$sc = new Scanner();
$N = $sc->nextInt();
$P = $sc->nextInt();

if ($N == 1) {
    echo $P . PHP_EOL;
    exit;
}
if ($P == 1) {
    echo 1 . PHP_EOL;
    exit;
}
$MAX = pow(10, 12);

$result = [];

while ( $P != 1 ) {
    if ($P % 2 == 0) {
        $result[] = 2;
        $P /= 2;
    }
    $i = 3;
    while ($i <= $MAX) {
        if ($P % $i == 0) {
            $result[] = $i;
            $P /= $i;
            break;
        }
        $i += 2;
    }
}
$list = [];
$ans = 1;
foreach($result as $v) {
    $list[$v]++;
    if ($list[$v] === $N) {
        $list[$v] = 0;
        $ans *= $v;
    }
}

echo $ans . PHP_EOL;

class Scanner {
    private $arr = [];
    private $count = 0;
    private $pointer = 0;
    public function next() {
        if($this->pointer >= $this->count) {
            $str = trim(fgets(STDIN));
            $this->arr = explode(' ', $str);
            $this->count = count($this->arr);
            $this->pointer = 0;
        }
        $result = $this->arr[$this->pointer];
        $this->pointer++;
        return $result;
    }
    public function hasNext() {
        return $this->pointer < $this->count;
    }
    public function nextInt() {
        return (int)$this->next();
    }
    public function nextDouble() {
        return (double)$this->next();
    }
}