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

public class Main{
    public static void main(String[] args)throws IOException {
       BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
       int test_case = Integer.parseInt(reader.readLine());
       for (int i=0; i<test_case; i++){
           String[]nums = reader.readLine().split(" ");
           solve(Integer.parseInt(nums[0]),Integer.parseInt(nums[1]));
       }
    }

    public static void solve(int n, int k){
        LinkedList<Integer> list = new LinkedList<Integer>();
        //right side
        for(int i=k+1; i<=n; i++){
            list.add(i);
        }  
        //left side
        Set<Integer>a = new HashSet<Integer>();
        for(int i=k-1; i>=1; i--){
            if(!a.contains(i)){
                a.add(k-i);
                list.add(i);
            }
        }
        System.out.println(list.size());
        if(list.size()>0){
            System.out.println(list.toString().replaceAll("[\\[\\],]",""));
        }
    }

  
}