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 PYTHON3):

Solution:
for t in range(int(input())):
	n,k = (input()).split()
	n = int(n)
	k = int(k)
	if n%2==0:
		if k<=n/2-1:
			possible = 1
		else :
			possible = 0
	else :
		if k<=int(n/2):
			possible = 1
		else :
			possible = 0

	if possible:
		not_peak = 1
		peak = n  # number to add at the peak positions
		for i in range(1,2*k+1):
			if i%2!=0:
				print(not_peak,end=' ')
				not_peak += 1
			else :
				print(peak, end=' ')
				peak -= 1
		for i in range(not_peak ,peak+1):
			print(not_peak,end=' ')
			not_peak += 1
		print()
	else :
		print(-1)