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>
using namespace std;
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define REP(i, k, n) for(int i = k; i < (int)(n); i++)
const int maxN = int(1e5 + 10);
int e[maxN] = {}, o[maxN] = {};
int num[maxN] = {};
using ll = long long;

int main() {
    ll n, m;
    ll ans = 0;
    cin >> n >> m;

    for(ll i = 1; i * i <= m; i++) {
        if(m % i == 0) {
            ll i1 = i, i2 = m / i;
            if(n * i1 <= m && ans < i1) {
                ans = i1;
            }
            if(n * i2 <= m && ans < i2) {
                ans = i2;
            }
        }
    }
    cout << ans << endl;
    return 0;
}