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.*;
import java.lang.StringBuilder;
import java.math.BigInteger;

public class Solution {
	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		while(t-- > 0) {
			int n = s.nextInt();
			int k = s.nextInt();
			System.out.println(n - (k % 2 == 0 ? k / 2 : k / 2 + 1));
			for(int i = k + 1; i <= n; i++) System.out.print(i + " ");
			for(int i = k % 2 == 0 ? k / 2 : k / 2 + 1; i <= k - 1; i++) System.out.print(i + " ");
			System.out.println();
		}
	}
}