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: Wrong Answer)

<?php
list($n, $m) = explode(" ", trim(fgets(STDIN)));
 
for($i = 2; $i <= sqrt($m); $i++){
    if($m % $i == 0){
        $f[] = $i;
        $f[] = $m / $i;
    }
}
sort($f);
$max = 0;
foreach($f as $F){
    if($F > $max && $F <= $m/$n){
        $max = max($max, $F);
    }
}
echo $max;