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 IOException {

        //write your code here
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while(t-->0) {
            long n = sc.nextLong();
            long k = sc.nextLong();
            long temp = k/ 2 , sum = 0;
            if(k%2==1)
                  temp++;
            sum = n - k ;
            sum += (k-temp) ;
            System.out.println(sum);
            for(long i=temp; i <= n; i++){
                    if(i!=k)
                         System.out.print(i+" ");
            }
            System.out.println();
        }
    }
}