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>

#define pb push_back
#define all(v) (v).begin() , (v).end()
#define popcnt(x) __builtin_popcount(x)
#define inf 0x3f3f3f3f
#define watch(x) cout << (#x) << " is " << (x) << endl
#define F first
#define S second

using namespace std;
typedef long long  ll;

int main() {
  int n , m;
  cin >> n >> m;
  vector<int> d;
  for(int i = 1 ; 1ll * i * i <= m ; ++i){
    if(m % i == 0){
      d.pb(i);
      if(i != m / i)d.pb(m / i);
    }
  }
  sort(all(d));
  int ans = 1;
  for(int x : d){
    if(m - x * n >= 0 && (m - x * n) % x == 0)ans = x;
  }
  cout << ans << '\n';
}