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 PHP (5.6.30) (judge verdict: Accepted)

<?php
//error_reporting(0);
//$N = trim(fgets(STDIN));
list($N,$M) = explode(" ",trim(fgets(STDIN)));
//$v = explode(" ",trim(fgets(STDIN)));

$re = 1;
for($A=1;$A * $A <= $M;$A++) {
  if ($M % $A != 0) continue;
  $B = floor($M / $A);
  if ($A * $N <= $M) $re = max($re,$A);
  if ($B * $N <= $M) $re = max($re,$B);
}
printf("%d\n",$re);