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: Accepted)

#include<stdio.h>
#include<stdlib.h>
#define ll long long
int upll(const void*a, const void*b){return*(ll*)a<*(ll*)b?-1:*(ll*)a>*(ll*)b?1:0;}
void sortup(ll*a,int n){qsort(a,n,sizeof(ll),upll);}

ll d[10000];
int cnt;
int main(){
	int n,m;
	scanf("%d%d",&n,&m);
	int i;
	for(i=1;i*i<m;i++)if(m%i==0){
		d[cnt++]=i;
		d[cnt++]=m/i;
	}
	if(i*i==m)d[cnt++]=m;
	sortup(d,cnt);
	int ans;
	for(int i=0;i<cnt;i++)if(d[i]<=m/n)ans=d[i];
	printf("%d",ans);
}