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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Test
{
    
    public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		try{
         Scanner s=new Scanner(System.in);
            int T=s.nextInt();
            for(int t=0;t<T;t++){
            
                int n=s.nextInt();
                int k=s.nextInt();
                int[] a=new int[n];
                int index=-1;
                for(int i=0;i<n;i++)
                {
                    a[i]=i+1;
                    if(a[i]==k)
                    index=i;
                }
                
                System.out.println(n-1-index+index-(int)Math.floor(index/2));
                
                for(int i=index-1;i>=Math.floor(index/2);i--)
                System.out.print(a[i]+" ");
                
                for(int i=index+1;i<n;i++)
                System.out.print(a[i]+" ");
                
                System.out.print("\n");
                
               
            }
        }
        catch(Exception e){
		    
		}
	}
}