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.*;
          
          public class T {
              public static void main(String[] args) throws IOException {
                  Scanner sc = new Scanner(System.in);
                  int loop = sc.nextInt();
                  List<String> ans = new ArrayList<>();
                  
                    while(loop-->0){  
                      int n = sc.nextInt();  
                      int k = sc.nextInt();     
                        HashSet<Integer> store = new HashSet<Integer>();

                      for(int i=k+1;i<=n;i++)store.add(i);
                        int next = 2;
                      for(int i=k-1;i>0;i--){
                        if(next+i>k)store.add(i);else break;
                        next = i;
                      }
                      
                      ans.add(String.valueOf(store.size()));
                      String x = "";
                      for(Integer as: store)x+=String.valueOf(as)+" ";
                    ans.add(x);
                    }
                    for(int ai=0;ai<ans.size();ai++)System.out.println(ans.get(ai));
          } 
 
}