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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.List;

public class Main {

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());

		while (t-- > 0) {
			String[] st = br.readLine().split(" ");
			int n = Integer.parseInt(st[0]);
			int k = Integer.parseInt(st[1]);

			StringBuilder sb = new StringBuilder();
			int count = 0;
			for (int i = k + 1; i <= n; i++) {
				sb.append(i + " ");
				count++;
			}

			for (int i = k - 1; i >= (k + 1) / 2; i--) {
				sb.append(i + " ");
				count++;
			}
			System.out.println(count);
			if (count > 0)
				System.out.println(sb);
		}
	}
}