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:
if __name__ == '__main__':
    for _ in range(int(input())):
        n, k = list(map(int, input().split()))

        if k == 0:
            print(' '.join(map(str, range(1, n + 1))))
        elif k > n // 2:
            print(-1)
        else:
            valid = True
            ans = [0] * n
            i = n - k + 1
            x = 1
            while i <= n and x <= len(ans):
                ans[x] = i
                if x == len(ans) - 1:
                    valid = False
                    break
                i += 1
                x += 2

            if not valid:
                print(-1)
                continue

            i = 1
            for x in range(len(ans)):
                if ans[x] == 0:
                    ans[x] = i
                    i += 1

            print(' '.join(map(str, ans)))