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 sys
# sys.stdin=open('input.txt','r')
# sys.stdout=open('output.txt','w')


def arrIn():
    return list(map(int,input().split()))
def mapIn():
    return map(int,input().split())
def check_palindrome(s):
    n=len(s)
    for i in range(n):
        if s[i]!=s[n-i-1]:return False
    return True

for ii in range(int(input())):
    n,p=mapIn()
    x=n//2
    # if n==1:
    #     print(a[i])
    #     continue
    x=n//2
    if n%2==0:x-=1
    # print(x)
    if p>x:print(-1)
    else:
        a=[0]*n
        c=0
        x=n
        if p!=0:
            for i in range(1,n,2):
                a[i]=x
                x-=1
                c+=1
                if c==p:
                    break
        y=1
        for i in range(n):
            if a[i]==0:
                a[i]=y
                y+=1
        for i in range(n):
            print(a[i],end=" ")
        print()