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>
#define Tree int h,int l,int r,int L,int R
#define left 2*h,l,(l+r)/2,L,R
#define right 2*h+1,(l+r)/2+1,r,L,R
#define F first
#define S second
#define Pb push_back
using namespace std;
long long n,m,A,B,ans;
main ()
{
	cin>>n>>m;
	
	for (int i=1; i<=sqrt(m); i++)
		if (m%i==0)
		{
			A=i;
			B=m/i;
			
			if (n*A<=m) ans=max(ans,A);
			if (n*B<=m) ans=max(ans,B);
		}
	
	cout<<ans<<endl;
}