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.util.Arrays;
import java.util.StringTokenizer;

public class A {

    public void solve() {
        int t = in.nextInt();

        while (t-- > 0) {
            int n = in.nextInt();
            int k = in.nextInt();

            int a[] = new int[n+1];
            int ans = n - 1;
            a[k] = -1;

            for (int i = k; i>=1; i--) {
                if (a[i] == -1) continue;
                if (i == k - i)
                    a[i] = 1;
                else {
                    a[i] = 1;
                    a[k - i] = -1;
                    ans--;
                }
            }

            out.println(ans);
            for (int i=1; i<=n; i++) {
                if (i>k)
                    out.print(i + " ");
                else if (a[i] > 0)
                    out.print(i+" ");
            }

            out.println();

        }
    }

    String input = "";
    String output = "";
    FastScanner in;
    PrintWriter out;

    void run() throws Exception {
        if (input.length() == 0) {
            in = new FastScanner(System.in);
        } else {
            in = new FastScanner(new File(input));
        }
        if (output.length() == 0) {
            out = new PrintWriter(System.out);
        } else {
            out = new PrintWriter(new File(output));
        }

        solve();

        out.close();

    }

    public static void main(String[] args) throws Exception {
        new A().run();
    }

    class FastScanner {

        BufferedReader bf;
        StringTokenizer st;

        public FastScanner(InputStream is) {
            bf = new BufferedReader(new InputStreamReader(is));
        }

        public FastScanner(File fr) throws FileNotFoundException {
            bf = new BufferedReader(new FileReader(fr));
        }

        public String next() {
            try {
                while (st == null || !st.hasMoreTokens()) {
                    st = new StringTokenizer(bf.readLine());
                }
            } catch (IOException ex) {
                ex.printStackTrace();
            }
            return st.nextToken();
        }

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

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

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

        public int[] readIntArray(int length) {
            int arr[] = new int[length];
            for (int i = 0; i<length; i++)
                arr[i] = nextInt();
            return arr;
        }
    }
}