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 C (Clang 3.8.0) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>

int main(void){

  int N,M;
  scanf("%d %d", &N, &M);

  int p=M/N,ans=1;

  while(p>0){
    if(M%p==0 && N*p<=M){
      printf("%d\n", p);
      return 0;
    }
    p--;
  }

  return 0;
}