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 Test {
public static void main(String[] args)
{
	Scanner input =new Scanner (System.in);
	int t=input.nextInt();
String output="";
	for(int i=1;i<=t;i++) {
	 int n=input.nextInt();
	 int k=input.nextInt();
	output+=fun(n,k)+"\n";
	}
	System.out.println(output);
}



public static String fun(int n,int k)
{	
int arr[]=new int[k];
int count=0;
	String output="";
	String res="";
	for(int i=n;i>=1;i--)
	{	if(i>k) {
		output+=i+" ";count++;
		}
	}
	
	for(int j=0;j<k;j++)
	arr[j]=j+1;
	
	for(int i=k-1;i>=0;i--)
	{
		for(int j=0;j<i;j++)
		{
			if(arr[i]+arr[j]==k &&(arr[j]!=-1 || arr[i]!=-1))
			{
				output+=arr[i]+" ";
				count++;
				arr[j]=-1;
				arr[i]=-1;
			}
		}
	}
	
	for(int j=0;j<k-1;j++)
		{
		if(arr[j]!=-1)
		{
			output+=arr[j]+" ";
		count++;
		}
		}
	
res=count+"\n"+output;
	return res;
	
}   


}