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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)



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

  int yakusu_count = 1;
  vector<long long> yakusu(n);
  yakusu.at(0) = m;
  int current = 1;

  for(int i = m - 1; i > 0; i--) {
    if(m % i == 0) {
      yakusu.at(current) = i;
      current++;
      yakusu_count++;
    }
  }

  bool flag = 0;
  
  rep(i,yakusu_count){
    if(m >= n * yakusu.at(i)) {
      cout << yakusu.at(i) << endl;
      flag = 1;
      break;
    }
  }

  if(flag == 0) cout << 1 << endl;
}