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.io.*;

public class Main {
	static final int M = 1000000007;
	static FastReader in = new FastReader();
//	static PrintWriter out = new PrintWriter(System.out);
//	static Scanner in = new Scanner(System.in);
//	File file = new File("input.txt");
//	Scanner in = new Scanner(file);
//	PrintWriter out = new PrintWriter(new FileWriter("output.txt"));
//	Arrays.sort(arr, Comparator.comparingDouble(o -> o[0])); // use as int[n][2];
//	static boolean[] prime = new boolean[1100001];
	public static void main(String[] args) {
		
		int t = in.nextInt();
		while(t-- > 0) {
			int n = in.nextInt(), k = in.nextInt();
			int size = n - (k-1)/2 - 1;
			System.out.println(size);
			if(size!=0) {
				for(int i = (k-1)/2 + 1; i<=n; i++) {
					if(i!=k) {
						System.out.print(i+" ");
					}
				}
				System.out.println();
			}
			
		}
	}
	
	static void sieve(int n, boolean[] prime)
    {
        for (int i = 0; i <= n; i++)
            prime[i] = true;
 
        for (int p = 2; p * p <= n; p++) 
        {
            if (prime[p] == true) 
            {
                for (int i = p * p; i <= n; i += p)
                    prime[i] = false;
            }
        }
    }
	static int gcd(int a, int b) {
		if(b==0) return a;
		return gcd(b, a%b);
	}
	
	static class Pair{
		int f;
		int s;
		public Pair(int x, int y){
			this.f = x;
			this.s = y;
		}
	}

	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;
		}
	}
}