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) {
		// InputStreamReader isr = new InputStreamReader(System.in);
		// BufferedReader br = new BufferedReader(isr);
		Scanner scanner = new Scanner(System.in);

		final int n = Integer.parseInt(scanner.nextLine());

		int[][] foo = new int[n][2];

		for (int i = 0; i < n; i++) {
			final String[] boo = scanner.nextLine().split(" ");
			foo[i][0] = Integer.parseInt(boo[0]);
			foo[i][1] = Integer.parseInt(boo[1]);
		}

		foo(foo);

	}

	public static void foo(int[][] values) {

		for (int[] value : values) {
			int n = value[0];
			int k = value[1];

			System.out.println(k / 2 + (n - k));

			for (int i = k / 2 + k % 2; i < k; i++) {
				System.out.print(i + " ");
			}

			for (int i = k + 1; i <= n; i++) {
				System.out.print(i + " ");
			}

			System.out.println();
		}

	}
}