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 Main
{
	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();
		    int k=sc.nextInt();
		    
		    solve(n,k);
		    System.out.println();
		}
		
	}
	public static void solve(int n,int k){
	    int count=0;
	    List<Integer> ans=new ArrayList<>();
	   
	    if(n==1 && k==1){ 
	        System.out.println(0);
	        return;
	    }
	    
	    
	    if(n>k){
	        for(int i=k+1;i<=n;i++){
	            ans.add(i);
	            count++;
	        }
	    }
	    
	    HashSet<Integer> nottoinclude=new HashSet<>();
	    
	    for(int i=k-1;i>0;i--){
	        if(!nottoinclude.contains(k-i)){ 
	            ans.add(i);
	            nottoinclude.add(i);
	            count++;
	        }
	    }
	    System.out.println(count);
	    for(int a:ans){
	        System.out.print(a+" ");
	    }
	}
}