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 INF 2147483647
#define INF_LL 9223372036854775807
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;

vector<int> ed(int n)//nの約数を列挙
{
	vector<int> ret;
	for (int i = 1; i*i <= n; ++i)
	{
		if (n%i == 0)
		{
			ret.push_back(i);
			if (i != 1 && i*i != n)
			{
				ret.push_back(n / i);
			}
		}
	}
	return ret;
}

int main() {
	int N, M;
	cin >> N >> M;
	vector<int> a = ed(M);
	ll ans = INF;
	for (int i = 0; i < a.size(); i++) {
		if (a[i] >= N && a[i] < ans)ans = a[i];
	}
	cout << M / ans << endl;
	return 0;
}