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: Time Limit Exceeded)

#include<iostream>
#include<cmath>
using namespace std;
long long n,m;
long long sol(long long n,long long m)
{
	long long ans;
	for(long long j=1;j<=m;j++)
	if(m%j==0&&j*n<=m)
	{
		if(j>ans) ans=j;
	}
	return ans;
}
int main(){
	cin>>n>>m;
	if(n>m) {
		cout<<"0"<<endl;
		return 0;
	}
	if(m%n==0) cout<<m/n<<endl;
	else
	cout<<sol(n,m)<<endl;
	return 0;
}