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;
int main(){
	int n,t;
	cin >> n>>t;
	if(t%n == 0) {
		cout << t/n << endl;
		return 0;
	}
	int m =t/n;
	vector<int> ret;
	for(int i=1 ; i*i<=t ; ++i)
	{
		if(t%i == 0)
		{
			ret.push_back(i);
			if(i!=1 && i*i!=t/n)
			{
				ret.push_back(t/i);
			}
		}
	}
	sort(ret.rbegin(),ret.rend());
  int i=0;	
  while(ret[i]>t/n)
    i++;
  cout<<ret[i]<<endl;
}