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;
#define rep(i,n) for(int i=0;i<n;i++)
#define ll long long

int gcd(int a, int b) 
{ 
    if (a == 0) 
        return b; 
    return gcd(b % a, a); 
} 
int findGCD(ll arr[], ll n) 
{ 
    ll result = arr[0]; 
    for (int i = 1; i < n; i++) 
    { 
        result = gcd(arr[i], result); 
  
        if(result == 1) 
        { 
           return 1; 
        } 
    } 
    return result; 
} 
int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	ll n,m,tmp=0;
	cin >> n >> m;
	ll a[n];
	rep(i,n){
		a[i] = m/n;
	}
	ll res = findGCD(a,n);
	tmp = m%n;
	cout << gcd(res,tmp) << endl;
	return 0;
}