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.Scanner;

public class A705 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t=sc.nextInt();
        while(t-- > 0){
            int n=sc.nextInt(),k=sc.nextInt();
            String ans = "";
            int c=0;
            int ceil = (int) Math.ceil((double)k/2);
            for(int i=1;i<=n;i++){
                if(i<ceil || i==k)
                    continue;
                c++;
                ans+=i+" ";
            }

            System.out.println(c);
            if(c>0){
                System.out.println(ans);
            }
        }
    }
}