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.*;
public class Test 
{
    public static void main(String[] args) 
    {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while (t-- > 0) 
        {
            int n = sc.nextInt(), k = sc.nextInt(), val = (int) Math.ceil((double) k / 2);
            List<Integer> ans = new ArrayList<>();
            for (int i = k - 1; i >= val; i--)
                ans.add(i);
            for (int i = k + 1; i <= n; i++)
                ans.add(i);
            System.out.println(ans.size());
            for (Integer i : ans)
                System.out.print(i + " ");
            System.out.println();
        }
    }
}