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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define lo long
const int lmax=1999999999;
const long long lmx=1999999999999999999;
long long n,m,ans;
vector<long long>v;
int main(){std::ios::sync_with_stdio(false);
cin>>n>>m;
for(long long i=1;i*i<=m;i++)
{
	if(m%i==0)
	{
		v.push_back(i);
		if(i!=m/i)
		{
			v.push_back(m/i);
		}
	}
}
sort(v.begin(),v.end());
for(int i=0;i<v.size();i++)
{
	long long q=m/v[i];
	if(q>=n)
	{
		ans=v[i];
	}
}
cout<<ans<<endl;
}
/*

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                       * *
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*/