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 trav(a, b) for(auto& a: b)
#define all(a) a.begin(), a.end()
#define gottagofast ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr)
using namespace std;
using ll = long long;
using ull = unsigned long long;

int main() {
	gottagofast;
	ll n, m;
	cin >> n >> m;
	ll ans = 1;
	for(ll i = 1; i * i <= m; ++i) {
		if(m % i == 0) {
			if(i * n <= m) {
				ans = max(ans, i);
			}
			if(i != m / i) {
				ll d = m / i;
				if(d * n <= m) {
					ans = max(d, ans);
				}
			}
		}
	}
	cout << ans;
	return 0;

}