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:
from sys import stdin#, setrecursionlimit
from heapq import heappush, heappop, heapify, heappushpop
#setrecursionlimit(1000000)
lines = stdin.read().splitlines()
li = -1
def inp(): global li; li += 1; return lines[li]
def inpint(): global li; li += 1; return int(lines[li])
def inpints(change = 0): global li; li += 1; return [int(i) + change for i in lines[li].split()]
def inpfloat(): global li; li += 1; return float(lines[li])
def inpfloats(change = 0): global li; li += 1; return [float(i) + change for i in lines[li].split()]


t = inpint()
for T in range(t):
    n, k = inpints()
    if k > n // 2 or (n % 2 == 0 and k >= n // 2):
        print(-1); continue

    arr = []
    for i in range(k):
        arr.append(i)
        arr.append(n - i - 1)
    for i in range(k, n - k):
        arr.append(i)
    print(*[i + 1 for i in arr])