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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <cmath>
#include <vector>
using namespace std;

int main() {
    int N, M;
    cin >> N >> M;

    vector<int> M_list;
    for (int i = 1; i * i <= M; i++) {
        if (M % i != 0) continue;
        M_list.push_back(i);
        if (M / i == i) continue;
        M_list.push_back(M / i);
    }

    int ans = 1;
    for (int i : M_list) {
        if (i <= M / N && i > ans) ans = i;
    }

    cout << ans << endl;
}