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.LinkedList;
import java.util.List;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);

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

            int totalCounter = 0;
            List<Integer> list = new LinkedList<>();
            for (int i = k + 1; i <= n; i++) {
                list.add(i);
                totalCounter++;
            }

            int back = k / 2;
            for (int i = 0; i < back; i++) {
                list.add(--k);
                totalCounter++;
            }


            System.out.println(totalCounter);
            for (int v : list) System.out.print(v + " ");
            System.out.println();


        }
        in.close();

    }

}