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.*;
import java.lang.*;
import java.io.*;
import java.math.*;
 
public class Main {
	public static void main (String[] args) {
		Scanner scan=new Scanner(System.in);
		int t=scan.nextInt();
		while(t-->0){
		    int n=scan.nextInt();
		    int k=scan.nextInt();
		
		    int count=n-k+k/2;
		    System.out.println(count);
		    for(int i=(k+1)/2;i<=n;i++){
		        if(i==k)   continue;
		        System.out.print(i+" ");
		    }
		    System.out.println();
		     
		}
	}	
		
	
}