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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;

public class a {
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader()
		{
			br = new BufferedReader(
				new InputStreamReader(System.in));
		}

		String next()
		{
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				}
				catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() { return Integer.parseInt(next()); }

		long nextLong() { return Long.parseLong(next()); }

		double nextDouble()
		{
			return Double.parseDouble(next());
		}

		String nextLine()
		{
			String str = "";
			try {
				str = br.readLine();
			}
			catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	public static void main(String[] args)
	{
		FastReader sc = new FastReader();
        int t=sc.nextInt();
        while(t-->0)
        {
            int n=sc.nextInt();
            int k=sc.nextInt();
            int cnt=n-k+(k/2);
            System.out.println(cnt);
            int m;
            if(k%2==0)
                m=k/2;
            else
                m=k/2+1;
            for(int i=m;i<=n;i++)
                if(i!=k)
                    System.out.print(i+" ");
            System.out.println();
        }
	}
}