Problem: A sequence of n integers is called a permutation if it contains all integers from 1 to n exactly once.

Given two integers n and k, construct a permutation a of numbers from 1 to n which has exactly k peaks. An index i of an array a of size n is said to be a peak if 1 < i < n and a_i \gt a_{i-1} and a_i \gt a_{i+1}. If such permutation is not possible, then print -1.

Input

The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases.

Then t lines follow, each containing two space-separated integers n (1 ≤ n ≤ 100) and k (0 ≤ k ≤ n) — the length of an array and the required number of peaks.

Output

Output t lines. For each test case, if there is no permutation with given length and number of peaks, then print -1. Otherwise print a line containing n space-separated integers which forms a permutation of numbers from 1 to n and contains exactly k peaks. 

If there are multiple answers, print any.

Example

Input


5
1 0
5 2
6 6
2 1
6 1


Output


1 
2 4 1 5 3 
-1
-1
1 3 6 5 4 2

Note

In the second test case of the example, we have array a = [2,4,1,5,3]. Here, indices i=2 and i=4 are the peaks of the array. This is because (a_{2} \gt a_{1} , a_{2} \gt a_{3}) and (a_{4} \gt a_{3}, a_{4} \gt a_{5}). 

Solution (in JAVA):

Solution:


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

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]);
			if (k == 0) {
				StringBuilder sn = new StringBuilder();
				for (int i = 1; i <= n; i++) {
					sn.append(i + " ");
				}
				System.out.println(sn);
				continue;
			}

			if (n < 3) {
				System.out.println(-1);
				continue;
			}

			int max = (n - 3) / 2 + 1;

			if (k > max) {
				System.out.println(-1);
				continue;
			}
			StringBuilder sb = new StringBuilder();
			if (k != 0) {
				sb.append(1 + " " + 3 + " " + 2 + " ");
				k--;
			} else {
				sb.append(1 + " " + 2 + " " + 3 + " ");
			}

			int temp = 4;
			while (k > 0) {
				sb.append((temp + 1) + " " + temp + " ");
				temp += 2;
				k--;
			}

			while (temp <= n) {
				sb.append(temp + " ");
				temp++;
			}

			System.out.println(sb);
		}
	}
}