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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.net.*;
import java.util.*;
import java.util.stream.IntStream;

/*
 *
 *  @author Sabirov Jakhongir
 *
 */
public class Java8 {
    static int x = 10;


    public static class ClassAuthenticator extends Authenticator
    {
        protected PasswordAuthentication getPasswordAuthentication()
        {
            this.show();
            String username = "javaTpoint";
            String password = "java";
            return new PasswordAuthentication(username, password.toCharArray());
        }
        void show()
        {
            int hostname = getRequestingPort();
            System.out.println("Port Requesting :" + hostname);
        }
    }
    static class Food{
        private String foodName;
        private int rating;

        public Food(String foodName, int rating) {
            this.foodName = foodName;
            this.rating = rating;
        }

        public String getFoodName() {
            return foodName;
        }

        public void setFoodName(String foodName) {
            this.foodName = foodName;
        }

        public int getRating() {
            return rating;
        }

        public void setRating(int rating) {
            this.rating = rating;
        }
    }

    public static void main(String[] args) {
       Scanner cin = new Scanner(System.in);
       int t = cin.nextInt();
       while (t -- > 0)
       {
           int n = cin.nextInt();
           int k = cin.nextInt();
           HashMap<Integer,Boolean> hashMap = new HashMap<>();
           for(int i = 1 ; i <= n ;i ++){
               hashMap.put(i,true);
           }
           hashMap.put(k,false);
           int cnt = 1;
           for(int i = 1 ; i < k ;i ++){
               int temp = k - i;
               if(temp + i == k && hashMap.get(temp) && hashMap.get(i) && temp != i){
                   hashMap.put(i, false);
                   cnt ++;
               }
           }
           System.out.println(n - cnt);
           hashMap.forEach((k1,v) ->{
               if(v){
                   System.out.print(k1 + " ");
               }
           });
           System.out.println();
       }

    }
    static int suma(int x){
        System.out.println(x);
        if(x == 0) return 0;
        return suma(x - 1) + x;
    }
}