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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

long long n,m;

long long gcd(long long x, long long y){
	//cout<<x<<" "<<y<<endl;
	if(y!=0){
		long long tmp=y;
		y=x%y;
		x=tmp;
		return gcd(x,y);
	}else{
		return x;
	}
}

int main(){
	cin>>n>>m;
	long long mm=m%n;
	long long nn=m/n;
	if(mm==0){
		cout<<nn<<endl;
	}else{
		mm+=nn;
		cout<<gcd(nn,mm)<<endl;
	}
}