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.LinkedList;
import java.util.Queue;
import java.util.Scanner;

public class Main {

	static Queue<Integer> q = new LinkedList<Integer>();

	static void Divisor(int M){
		for(int i=1; i<Math.sqrt(M); i++) {
			if(M%i!=0)	continue;
			q.add(i);
			q.add(M/i);
		}
		if(M%Math.sqrt(M) == 0)	q.add((int) Math.sqrt(M));
	}

    public static void main(String[] args) throws Exception {
    	try(Scanner sc = new Scanner(System.in)) {

    		int N = sc.nextInt();
    		int M = sc.nextInt();
    		Divisor(M);
    		N = M/N;
    		int max = 0;
    		while(!q.isEmpty()) {
    			int s = q.remove();
    			if(s > N)	continue;
    			max = s;
    		}
    		System.out.println(max);

    	}
    }
}