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 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();
			if(n==1) {
				System.out.println(0);
				continue;
			}
			String str;
			int x = 0;
			if(k%2==0) {
				System.out.println(n-(k/2));
				x=n-(k/2);
			}
			if(k%2==1) {
				System.out.println(n-k/2-1);
				x=n-k/2-1;
			}
			for(int i = n;i>=n-x;i--) {
				str = i==n-x?"\n":" ";
				if(i!=k) {
					System.out.print(i+str);
				}
			}
		}
	}
}