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

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

$ans = 1;
for ($i = 1; $i ** 2 <= $m; $i++) {
    if ($m % $i === 0) {
        if (intdiv($m, $i) >= $n) {
            $ans = max($ans, $i);
        }
        if ($i >= $n) {
            $ans = max($ans, intdiv($m, $i));
        }
    }
}

echo $ans;