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>

int gcm(int a,int b){
	int r,tmp;
	if(a<b){
		tmp=a;
		a=b;
		b=tmp;
	}
	
	r=a%b;
	while(r!=0){
		a=b;
		b=r;
		r=a%b;
	}
	return b;
}

int main(){
	int N,M,ans;
	scanf("%d%d",&N,&M);
	if(gcm(N,M)==1){
		printf("1\n");
		return 0;
	}
	
	for(int i=1;i<=M/N;i++){
		if(M%i==0)ans=i;
	}
	printf("%d\n",ans);
	return 0;
}