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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <algorithm>
#include <iostream>
#include <map>
#include <tuple>
#include <vector>

#define rep(i, n) for (int i = 0; (i) < (n); (i)++)
using namespace std;
using ll = long long;

int main(void) {
    int N, M;
    cin >> N >> M;
    int r = 0;
    for(int ret=1; ret <M; ++ret) {
        auto cand = M - ret * (N-1);
        if(cand <= 0)
            break;
        if(cand % ret == 0)
            r = ret;
    }
    cout << r << endl;

    return 0;
}