Problem: You are given two integers n and k. You are asked to choose maximum number of distinct integers from 1 to n so that there is no subset of chosen numbers with sum equal to k.

A subset of a set is a set that can be obtained from initial one by removing some (possibly all or none) elements of it.

Input

The first line contains the number of test cases T (1 ≤ T ≤ 100).

Each of the next T lines contains two integers n and k (1 ≤ k ≤ n ≤ 1000) — the description of test cases.

Output

For each test case output two lines. In the first line output a single integer m — the number of chosen integers.

In the second line output m distinct integers from 1 to n — the chosen numbers.

If there are multiple answers, print any. You can print the numbers in any order.

Example

Input


3
3 2
5 3
1 1


Output


2
3 1 
3
4 5 2 
0

Solution (in JAVA):

Solution:
import java.util.*;
public class CodeForces
{
    public static void main(String args[])
    {
    	Scanner sc = new Scanner(System.in);
    	int T = sc.nextInt();
    	for(int I = 0;I<T;I++)
    	{
    		int n = sc.nextInt(),k = sc.nextInt();
    		System.out.println(n - (int)Math.ceil(k/(double)2));
    		for(int i = (int)Math.ceil(k/(double)2);i<=n;i++)
    		{
    			if(i != k)
    			{
    				System.out.print(i+" ");
    			}
    		}
    		System.out.println();
    	}
    }
}