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 <iostream>
#include <string>
#include <sstream>
#include <vector>
#include <tuple>
#include <algorithm>
using namespace std;

int main() {
	long long N,M;
	cin >> N >> M;

	long long ans = 0;
	long long sigma_m = 0;
	for (long long i = 1; i*i <= M; i++) {
		if (M%i == 0) {
			sigma_m = M / i;
			if (N <= sigma_m) {
				ans =max(ans, i);
			}
			if (i >= N && sigma_m >= i && M%sigma_m == 0) {
				ans = max(ans,sigma_m);
			}
		}
	}	

	cout << ans;

	return 0;
}