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.io.*;

public class Main {
	public static void main(String[] args) throws NumberFormatException,IOException {
		
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		
		int t=Integer.parseInt(br.readLine());
		
		while(t-->0) {
			
			String[] temp=br.readLine().split(" ");
			int n=Integer.parseInt(temp[0]);
			int k=Integer.parseInt(temp[1]);
			
		    int ans=(n-k)+k/2;
		    System.out.println(ans);
		    
		    for(int i=k-1;i>=(k-(k/2));i--) {
		    	System.out.print(i+" ");
		    }
		    
		    for(int i=k+1;i<=n;i++) {
		    	System.out.print(i+" ");
		    }
		    System.out.println();
		}
	}
}