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:



class Solution:
    def generate_permutation_with_peaks(self, length, peaks_count):
        possible_peaks_count = length - peaks_count - 1
        if possible_peaks_count < peaks_count:
            return
        
        permutation = [-1 for i in range(length)]
        peaks_left = peaks_count
        simple_value = 1
        peak_value = length
        for i in range(length):
            is_peak = i % 2 != 0 and peaks_left > 0
            if is_peak:
                value = peak_value
                peak_value -= 1
                peaks_left -= 1
            else:
                value = simple_value
                simple_value += 1

            permutation[i] = value


        return permutation


s = Solution()

def permutation_to_string(permutation):
    return ' '.join(map(str, permutation))


t = int(input())
for i in range(t):
    n, k = map(int, input().split())
    permutation = s.generate_permutation_with_peaks(n, k)
    if permutation:
        print(permutation_to_string(permutation))
    else:
        print(-1)