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:
import math
n = int(input())
for i in range(n):
    a = list(map(int,input().strip().split()))
    
    # if a[1] > k: 
    #     l = []
    #     for i in range(1, a[0]-a[1]+1):
    #         l.append(i)
    #     # for i in range(a[0]-1, a[0]-1-a[1], -1):
    #     #     l = l.remove(l[i])
    #     t = []
    #     for i in range(a[0]-a[1]+1, a[0]+1):
    #         # for j in range(0, len(l), 2):
    #         #     l.insert(j,i)
    #         t.append(i)
    #     for i in range(0, a[0]//2):
    #         l.insert(i+i+1,t[i])    
    #     print(*l)
    # else:
    #     print(-1)
    # if a[1] == 0:
    #     l  = []
    #     for i in range(1, a[0]):
    #         l.append(i)
    #     print(l)
    if 2*a[1] < a[0]:
        l = []
        t = []
        c = 0
        for i in range(1, a[0]-a[1]+1):
            l.append(i)
        for j in range(a[0]-a[1]+1, a[0]+1):
            t.append(j)
        for i in range(0, len(t)):
            l.insert(i+i+1,t[i])
        
        for i in range(1, len(l)-1):
            if l[i-1] < l[i] and l[i+1] < l[i]:
                c+=1
        if c == a[1]:
            print(*l)
        else:
            print(-1)
            
    else:
        print(-1)