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.math.BigDecimal;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.Scanner;
import java.util.Vector;

public class Main {

	public static void main(String[] args) {
		Scanner ob = new Scanner(System.in);
		int t = ob.nextInt();
		for (int ii = 0; ii < t; ii++) {
			int n = ob.nextInt();
			int k = ob.nextInt();
			if ((k*2+1)>n) {
				System.out.println("-1");
			} else {
				int a[] = new int[n];
				int i = 1;
				int n1 = n;
				while (k != 0) {
					a[i] = n1;
					n1--;
					k--;
					i+=2;
				}
				//System.out.println(n1);
				//System.out.println(a[n-1]);
				for (int i1 = 0; i1 < n; i1++) {
					if(a[i1]==0){
					a[i1] = n1;
					n1--;
					}
				}
				for (int i1 = 0; i1 < n; i1 ++) {
					System.out.print(a[i1] + " ");
				}
				System.out.println();
			}
		}
	}
}