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.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Kanpsack
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
	Scanner sc= new Scanner(System.in);
	int t= sc.nextInt();
	while(t-->0){
	    int n= sc.nextInt();
	    int k= sc.nextInt();
	    int count= n-k+k/2;
	    System.out.println(count);
	    for(int i=k+1;i<=n;i++)
	        System.out.print(i+" ");
	    for(int j=(k+1)/2;j<k;j++)
	        System.out.print(j+" ");
	    System.out.println();
	}
	}
}