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<cstdio>
#include<vector>
std::vector<int> p;
int n,m,ans;
int main()
{
	scanf("%d%d",&n,&m);
	for (int i=1;i*i<=m;i++)
	    if (m%i==0)
	    {
		    p.push_back(i);
		    if (i*i!=m) p.push_back(m/i); 
	    }
	for (int i=0;i<p.size();i++) if (p[i]>ans&&p[i]*n<=m) ans=p[i];
	printf("%d\n",ans);
	return 0;
}