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: Accepted)

import java.util.*;

class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = Integer.parseInt(sc.next());
		int M = Integer.parseInt(sc.next());
		ArrayList<Integer> diviser_list = divise(M);
		Collections.reverse(diviser_list);
		for (int i=0;i<diviser_list.size();i++) {
			if (M/diviser_list.get(i)>=N) {
				System.out.println(diviser_list.get(i));
				break;
			}
		}
	}

    static ArrayList<Integer> divise(int n) {
    	ArrayList<Integer> list = new ArrayList<Integer>();
        for (int i=1;i<=Math.sqrt(n);i++) {
            if (n%i==0) {
                list.add(i);
                if (i*i!=n) {
					list.add(n/i);
                }
            }
        }
        Collections.sort(list);
                return list;
    }
}