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 5.4.1) (judge verdict: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;


#define all(c) (c).begin(),(c).end()
#define loop(s) for(int i = 0; s > i; i++)
#define repp(i,o,q) for(int i = o; q >= i; i++)
#define rep(i,q) for(int i = 0; (q) > i; i++)
#define pb push_back
#define MAX 1000000000
#define mod 1000000007

int main(){
  int N,M;
  cin >> N >> M;
  int saidai = M/N;
  int ok = 1;
  repp(i,1,saidai){
    if(M%i == 0) ok = i;
  }
  cout << ok << endl;
}