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;

int main() {
    int n, m;
    cin >> n >> m;
    int ans = 1;
    vector<int> fact;
    for (int i = 2; i <= sqrt(m); i++) {
        while(m % i == 0) {
            fact.push_back(i);
            m /= i;
        }
    }
    if (m != 0)
        fact.push_back(m);
    if (fact.size() == 1){
        cout << 1;
        return 0;
    }
    return 0;
    for (int i = 1; i <= 100100; i++) {
        if ((m - i) > 0 && ((m - i) % (n - 1)) == 0 && (m - i) / (n - 1) != 0){
            ans = max(ans, __gcd(i, (m - i) / (n - 1)));
            cout << "TRY THIS:" << i << ' ' << (m - i) / (n - 1) << ' ' << " ANS:" << ans << endl;
        }
    }
     cout <<  ans;
}