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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String args[]) {

		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		int M = sc.nextInt();

		List<Integer> x = new ArrayList<>();
		for (int i = 1; i <= M / 2; i++) {
			if (M % i == 0) {
				x.add(i);
				x.add(M / i);
			}
		}
		Collections.sort(x);

		int ans = 0;
		for (int i = 0; i < x.size(); i++) {
			if(M/x.get(i) >= N && x.get(i) >= ans) {
				ans = x.get(i);
			}
		}

		System.out.println(ans);
	}
}