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.lang.*;
import java.util.*;

public class A1493 {
    public static void main(String[] args) throws IOException{
        StringBuffer ans = new StringBuffer();
        StringTokenizer st;
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        st = new StringTokenizer(f.readLine());
        int t = Integer.parseInt(st.nextToken());
        for(int i = 0; i < t; i++){
            st = new StringTokenizer(f.readLine());
            int n = Integer.parseInt(st.nextToken());
            int k = Integer.parseInt(st.nextToken());
            ArrayList<Integer> arrl = new ArrayList<>();
            int r = k/2;
            if(k % 2 != 0)
                r++;
            for(int x = r; x <= n; x++){
                if(x == k)
                    continue;
                arrl.add(x);
            }
            ans.append(arrl.size());
            ans.append("\n");
            for(int x = 0; x < arrl.size(); x++){
                ans.append(arrl.get(x));
                ans.append(" ");
            }
            ans.append("\n");
        }
        f.close();


        System.out.println(ans);
    }
}