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.*;
public class Main{
    public static void main(String args[]){
        Scanner sc=new Scanner(System.in);
        int T=sc.nextInt();
        while(T-->0){
            int n=sc.nextInt();
            int k=sc.nextInt();
            HashSet<Integer> h=new HashSet<Integer>();
            h.add(k);
            for(int i=1;i<=k;i++){
                if(i!=k-i&&!h.contains(k-i))
                h.add(i);
            }
            System.out.println(n-h.size());
            if(n-h.size()!=0){
            for(int i=1;i<=n;i++){
                if(!h.contains(i))
                {System.out.print(i+" ");}
            }
System.out.println();
            }
        }
    }
}