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<iostream>
#include<string>
#include<algorithm>
#include<vector>
using namespace std;

int main() {
  long long n, m;
  int ans;
  cin >> n >> m;

  for(int i = 1; i <= m/2;i++) {
    if(m % i == 0){
      int j = m - m*n/i;
      if(j >= 0 && j % (m/i) == 0){
        cout << m/i << endl;
        return 0;
      } else {
        int j = m-i*n;
        if(j >= 0 && j % i == 0) ans = i;
      }
    }
  }
  cout << ans << endl;

  return 0;
}