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 <algorithm>
#include <climits>
#include <cmath>
#include <csignal>
#include <cstdio>
#include <cstdlib>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <string>
#include <tuple>
#include <vector>

using Graph = std::vector<std::vector<int>>;
using WGraph = std::vector<std::vector<std::pair<int, long long>>>;
using ll = long long;
using namespace std;

int main() {
    ll n = 0, m = 0;
    cin >> n >> m;
    ll ans = 0;
    for (ll i=1; i<=sqrt(m); i++) {
        if (m%i == 0) {
            ll tmp = m/i;
            if (i >= n) {
                ans = max(ans, tmp);
            }
            else if (tmp >= n) {
                ans = max(ans, i);
            }
        }
    }
    cout << ans << endl;
    return 0;
}