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 whatever //do not write package name here */

import java.io.*;
import java.util.*;


public class GFG {
	public static void main (String[] args) {
	    Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t!=0){
		    t--;
		    int n = sc.nextInt();
		    int k = sc.nextInt();
		    int p=0;
		    if(n>k)
		    p=n-k;
		    p+=k/2;
		    System.out.println(p);
		    if(p>0){
		        for(int i=n;i>k;i--){
		            System.out.print(i+" ");
		        }
		        if(k%2==0){
		            for(int i=k/2;i<k;i++){
		            System.out.print(i+" ");
		        }
		        }
		        else{
		            for(int i=(k/2)+1;i<k;i++){
		            System.out.print(i+" ");
		        }
		        }
		        System.out.println("");
		        
		    }
		}
	}
}