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:
//package codeforces._705;

import java.io.*;
import java.util.StringTokenizer;

public class _A {

    public static void main (String[] args) throws Exception {

        String s = "3\n" +
                "3 2\n" +
                "5 3\n" +
                "1 1";

//        br = new BufferedReader(new StringReader(s));
        br = new BufferedReader(new InputStreamReader(System.in));
        bw = new BufferedWriter(new OutputStreamWriter(System.out));

        rl(); int T = nin();
        next_test:
        for (int t=1; t<=T; ++t) {
            rl(); int n=nin(), k=nin();
            int c =0;
            int from = k/2;
            if (k%2==1) ++from;
            StringBuffer sb = new StringBuffer();
            for (int i=from; i<k; ++i) {
                sb.append(i+" ");
                ++c;
            }
            for (int i=k+1; i<=n; ++i) {
                sb.append(i+" ");
                ++c;
            }
            bw.write(c + "\n");
            if (c>0) bw.write(sb + "\n");
        }
        bw.flush();
    }

    static BufferedReader br; static BufferedWriter bw; static StringTokenizer st;
    static void rl() throws Exception{ st = new StringTokenizer(br.readLine()); }
    static long nlo(){ return Long.parseLong(st.nextToken()); }
    static int nin(){ return Integer.parseInt(st.nextToken()); }
    /*private static void te(){}*/
    static double ndo(){ return Double.parseDouble(st.nextToken()); }
    static char[] nca(){ return st.nextToken().toCharArray(); }
}