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:
/*package whatever //do not write package name here */
import java.util.*;
import java.io.*;

public final class Main {
	public static void main (String[] args) {
	    Scanner sc = new Scanner(System.in);
	    int t = sc.nextInt();
	    while(t-->0) {
	        int n = sc.nextInt();
	        int operations = sc.nextInt();
	        if(operations>(n-1)/2) {
	            System.out.println(-1);
	            continue;
	        }
	        int[] ans = new int[n];
	        int start = n;
	        for(int i = 1; i<n && operations>0; i+=2) {ans[i] = start--; operations--;}
	        for(int i = 0; i<n; i++) if(ans[i]==0) ans[i] = start--;
	        for(int i: ans) System.out.print(i + " ");
	        System.out.println();
	    }
	}
}