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
import java.util.*;

public class contest705div2_A {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int test = in.nextInt();
        StringBuilder sb = new StringBuilder();
        while(test-->0){
            int count =0;
            int n = in.nextInt();
            int k = in.nextInt();
            int m = n-k + k/2;
            sb.append(m+"\n");
            for(int i =k+1;i<=n;i++) sb.append(i+" ");
            for(int i=(k+1)/2;i<k;i++) sb.append(i+"\n");
        }
        System.out.println(sb.toString());
    }
}