Problem:
Score : 400 points

Problem Statement

You are given integers N and M.

Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

N \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.

Sample Input 1

3 14

Sample Output 1

2

Consider the sequence (a_1, a_2, a_3) = (2, 4, 8). Their greatest common divisor is 2, and this is the maximum value.

Sample Input 2

10 123

Sample Output 2

3

Sample Input 3

100000 1000000000

Sample Output 3

10000

Solution in PHP7 (7.0.15) (judge verdict: Accepted)

<?php

function divisors($N) {
    $res = array();
    for ($d = 1; $d*$d <= $N; $d++) {
        if ($N % $d == 0) {
            array_push($res, $d);
            if ($N / $d != $d) {
                array_push($res, $N / $d);
            }
        }
    } 
    return $res;
}

$input = explode(' ', trim(fgets(STDIN)));
$N = (int)$input[0];
$M = (int)$input[1];

$max = 0;
foreach (divisors($M) as $d) {
    if ($M / $d >= $N) {
        $max = max($max, $d);
    }
}

echo $max;