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 _ in range(int(input())):
    n,k=map(int,input().split())
    arr=[]
    count=0
    j=0
    if k==0:
        for aa in range(1,n+1):
            print(aa,end=' ')
        print()
    else:

        for i in range(1,n+1):
            if j==2:
                count+=1
                j=0
        
        
            arr.append(count)
            j+=1
        if arr[n-1]>=k:
            arrr=[1]
            l=1
            p=3
            q=2

            while l<n:
                for s in range(p,n+1,2):
                    arrr.append(s)
                    p=s+2
                    break
                for ss in range(q,n+1,2):
                    arrr.append(ss)
                    q+=2
                    break
                l+=2
       
            sss=0
            x=0
            y=0
        
            for kk in range(1,n-1):
            
                if arrr[kk]>arrr[kk-1] and arrr[kk]>arrr[kk+1]:
               
                
                    
                    sss+=1
               
                    if k==sss:
                        x=arrr[kk+1]+1
                        y=kk+1
                   

                        break
            jj=[]
            for hh in range(y+1):
                jj.append(arrr[hh])
  
            for g in range(x+1,n+1):
                jj.append(g)
            print(*jj)
        else:
            print(-1)