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 PYTHON):

Solution:
#####################################   
import atexit, io, sys, collections, math, heapq, fractions, bisect,copy
buffer = io.BytesIO() 
sys.stdout = buffer
@atexit.register 
def write(): sys.__stdout__.write(buffer.getvalue())   
####################################


def f(n,k):

	i = 1
	r= [-1 for _ in range(n)]
	for u in range(n, n - k, -1):
		if i < len(r):
			r[i] = u
		else:
			print -1
			return 
		i += 2
	i = 0
	for u in range(n- k, 0, -1):
		while(i < len(r) and r[i] != -1):
			i+=1
		r[i] = u
		i+=1

	count = 0
	for i in range(1, len(r)-1):
		count += 1 if r[i-1] < r[i] > r[i+1] else 0
	if count != k:
		print -1
		return 
	print ' '.join(map(str, r))
	return 


for u in range(int(raw_input())):
	n,k = map(int, raw_input().split())
	f(n,k)