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
import bisect
input_=lambda: sys.stdin.readline().strip("\r\n")
from math import log
from math import gcd
sa=lambda :input_()
sb=lambda:int(input_())
sc=lambda:input_().split()
sd=lambda:list(map(int,input_().split()))
se=lambda:float(input_())
sf=lambda:list(input_())
flsh=lambda: sys.stdout.flush()
#sys.setrecursionlimit(10**6)
mod=10**9+7
gp=[]
cost=[]
dp=[]
mx=[]
def dfs(root,par):
    global gp,cost,dp
    dp[root]=cost[root]
    for i in gp[root]:
        if i==par:continue
        dfs(i,root)
        dp[root]=max(dp[root],dp[i])
def hnbhai():
    n,k=sd()
    ans=[-1]*n
    abe=n
    x=k
    for i in range(1,n-1,2):
        if x==0:
            break
        ans[i]=abe
        abe-=1
        x-=1
    if x>0:
        print(-1)
        return
    for i in range(n):
        if ans[i]==-1:
            ans[i]=abe
            abe-=1
    print(*ans)
for _ in range(sb()):
    hnbhai()