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.lang.*;
import java.io.*;
public class Solution {

    public static void main(String[] args) throws IOException {
        Scanner scanner=new Scanner(System.in);
        int t=scanner.nextInt();
        while (t-->0){
            int n=scanner.nextInt();
            int k=scanner.nextInt();
            int val=(int)(Math.ceil(k/2.0));
            List<Integer> a=new ArrayList<>();
            for(int i=k-1;i>=val;i--)
                a.add(i);
            for(int i=k+1;i<=n;i++)
                a.add(i);
            System.out.println(a.size());
            for(int i:a)
                System.out.print(i+" ");
            System.out.println();
        }
    }
}