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 i in range(int(input())):
    a,b=map(int,input().split())
    x=[]
    if b==0:
        for j in range(1,a+1):
            x.append(j)
    else:
        if b>=a/2:
            x.append(-1)
        else:
            if a%2==0:
                count=0
                cnt=1
                for j in range(int(a/2),0,-1):
                    x.append(j)
                for j in range(a,a-b,-1) :
                    x.insert(cnt, j)
                    cnt += 2
                    count += 1
                for j in range(a // 2+1,a-b+1) :
                    x.append(j)
            else:
                cnt = 1
                count=0
                for j in range(a//2, 0, -1) :
                    x.append(j)
                for j in range(a, a-b, -1) :
                    x.insert(cnt, j)
                    cnt += 2
                    count+=1
                for j in range(a//2+1,a-b+1):
                    x.append(j)


    y=[]
    for _ in x:
        y.append(str(_))
    print(' '.join(y))