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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
 //Compiler version g++ 6.3.0

 int main()
 {
 	int a,b,c,d;
 	cin >> b>>a;
 	if(a==b){
 		cout << 1 << endl;
 	}else{
 	for (int i = 0; i <= a-b; i++) {
 		c=a/(b+i);
 		d=a%(b+i);
 		if(d==0){
 			break;
 		}}
 		if(!d==0){
 			cout << 1 << endl;
 		}else{
 		cout << c << endl;
 		}
 }}