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: Time Limit Exceeded)

<?php
list($n,$m)=explode(" ",trim(fgets(STDIN)));
if($m%$n==0){
  echo $m/$n;
}elseif($n==2){
  echo 1;
}else{
  $s=ceil($m/$n);
  $ans=1;
  $i=1;
  while($i<=$s){
    if($m%$i==0){
      if($m/$i>=$n){
      $ans=max($ans,$i);
    }else{
        $i=$s+1;
        break;
      }
    }
    ++$i;
  }
  echo $ans;
}