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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
long long MAX(long long a,long long b){return a<b?b:a;}
int main(){
  long long a=0,n,m,i,ans=1;
  scanf("%lld %lld",&n,&m);
  for(i=2;i*i<=m;i++){
    if(m%i)continue;
    if(i  *n<=m)a=MAX(a,i  );
    if(m/i*n<=m)a=MAX(a,m/i);
  }
  printf("%lld\n",a);
  return 0;
}
//i*n<=m m%i==0 MAX i