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:
# cook your dish here
t=int(input())
for i in range(t):
    inp=list(map(int,input().split()))
    n=inp[0]
    k=inp[1]
    val=n
    idx=0
    res=[]
    peak=0
    l=[i for i in range(1,n+1)]
    for i in range(n):
        res.append(0)
    if(n==k):
        print(-1)
    elif(n<=2 and k>0):
        print(-1)
    elif(k==0):
        for i in range(1,n+1):
            print(i,end=" ")
        print()
    elif((n-2)%2==0):
        if(((n-2)//2)<k):
            print(-1)
        elif(((n-2))//2>=k):
            for i in range(n):
                if(i%2!=0 and i<n-1):
                    res[i]=val
                    l.remove(val)
                    val=val-1
                    peak=peak+1
                    if(peak==k):
                        break
            for i in range(n):
                if(i%2==0 or i==n-1 or res[i]==0):
                    res[i]=l[idx]
                    idx=idx+1
            for item in res:
                print(item,end=" ")
            print()
        else:
            print(-1)
    else:
        if(((n-2)//2)<k-1):
            print(-1)
        elif(((n-2)//2)>=k-1):
            
            for i in range(n):
                if(i%2!=0 and i<n-1):
                    res[i]=val
                    l.remove(val)
                    val=val-1
                    peak=peak+1
                    if(peak==k):
                        break
            for i in range(n):
                if(i%2==0 or i==n-1 or res[i]==0):
                    res[i]=l[idx]
                    idx=idx+1
            for item in res:
                print(item,end=" ")
            print()
        else:
            print(-1)