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 <iostream>
#include <string>
#include <algorithm>
using namespace std;
typedef long long ll;

/*sortの仕方
 * ■ string s の場合
 * 昇順: sort(s.begin(), s.end())
 * 降順:  sort(s.rbegin(), s.rend())
 *
 * ■ int a[N] の場合
 * 昇順: sort(a, a+N)
 * 降順: 不明
 */

/*int alph2int(char character) {
    int x = character - 'a';
    return x;
}
*/

int main(){
	int N, M;
	cin >> N >> M;
	int ans = 0;
	for(int i = 1; i <= M/2; i++){
		if(M%i == 0){
			if(N <= M/i){
				ans = i;
			}
		}
	}

	cout << ans << endl;
	return 0;
}