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:
t=int(input())


def f(x):
    y=x.split(" ")
    for i in range(len(y)):
        y[i]=int(y[i])
    n=y[0]
    k=y[-1]
    if n%2==0:
        if k>=n/2:
            return [-1]
        else:
            l=[]
            i=0
            while(i<n):
                j=i+1
                l=l+[j]
                i+=1
            I=0
            i=1
            while(I<k):
                (l[i],l[i+1])=(l[i+1],l[i])
                i+=2
                I+=1
            return l            
    else:
        if k>n//2:
            return [-1]
        else:
            L=[]
            i=0
            while(i<n):
                j=i+1
                L=L+[j]
                i+=1
            I=0
            i=1
            while(I<k):
                (L[i],L[i+1])=(L[i+1],L[i])
                i+=2
                I+=1
            return L          

def g(x):
    i=0
    s=""
    for i in range(len(x)):
        s+=str(x[i])+" "
    return s
        
    
lines=""
ans=""
for i in range(t):
    x=input()
    lines+=x+"\n"
    ans+=g(f(x))+"\n"

print(ans)