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: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i, n) for(ll i = 0; i < (ll)(n); i++)
#define rep2(i, a, n) for(ll i = a; i < (ll)(n); i++)
#define memi cout << endl
#define kono(n) cout << fixed << setprecision(n)
#define all(c) (c).begin(), (c).end()
#define pb push_back
#define hina cout << ' '
#define in(n) cin >> n
#define in2(n, m) cin >> n >> m
#define in3(n, m, l) cin >> n >> m >> l
#define out(n) cout << n
const ll mei = (ll)1e9 + 7;

int main(){
  ll n, m, a;
  in2(n, m);
  rep2(i, 1, 105000000){
    if(m % i == 0){
      if(n * i <= m)
        a = max(a, i);
      if(n * (m / i) <= m)
        a = max(a, (m / i));
    }
  }
  out(a);
  memi;
}