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 (7.4.4) (judge verdict: Accepted)

<?php
  list($n,$m) = explode(" ", trim(fgets(STDIN)));

  if($n==1) {
    echo $m;
    exit;
  }

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