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 Solution
{
  public static void main(String args[]) throws Exception
  {
    BufferedReader Rb = new BufferedReader(new InputStreamReader(System.in));
    int count = Integer.valueOf(Rb.readLine());
    int counter = 0;
    while(counter++<count)
    {
      String temp[] = Rb.readLine().split(" ");
      int n = Integer.valueOf(temp[0]);
      int k = Integer.valueOf(temp[1]);
      int m = n - k + k - k / 2 - 1 + (k % 2 == 0?1:0);
      System.out.println(m);
      for(int i = (k % 2 == 0?k / 2:k / 2 + 1); i <= n; i++)
      {
        if(i == k)
        {continue;}
        System.out.print(i + " ");
      }
    }
  }
}