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:
#------------------Important Modules------------------#
from sys import stdin,stdout
from bisect import bisect_left as bl
from bisect import bisect_right as br
from heapq import *
from random import *
input=stdin.readline
prin=stdout.write
from random import sample
from collections import Counter,deque
from fractions import *
from math import sqrt,ceil,log2,gcd,cos,pi
#dist=[0]*(n+1)
mod=10**9+7
"""
class DisjSet: 
    def __init__(self, n): 
        
        self.rank = [1] * n 
        self.parent = [i for i in range(n)] 
    def find(self, x): 
        if (self.parent[x] != x): 
              
             

            self.parent[x] = self.find(self.parent[x]) 
              
            
        return self.parent[x] 
  
  
    
    def union(self, x, y): 
          
         
        xset = self.find(x) 
        yset = self.find(y) 
  
        if xset == yset: 
            return
  
        if self.rank[xset] < self.rank[yset]: 
            self.parent[xset] = yset 
  
        elif self.rank[xset] > self.rank[yset]: 
            self.parent[yset] = xset 
  
        else: 
            self.parent[yset] = xset 
            self.rank[xset] = self.rank[xset] + 1
  

"""

def f(arr,i,j,d,dist):
    if i==j:
        return 
    nn=max(arr[i:j])
    for tl in range(i,j):
        if arr[tl]==nn:
            dist[tl]=d
            #print(tl,dist[tl])
            f(arr,i,tl,d+1,dist)
            f(arr,tl+1,j,d+1,dist)
    #return dist
            
        
def ps(n):
    cp=0;lk=0;arr={}
    #print(n)
    #cc=0;
    while n%2==0:
        n=n//2
        #arr.append(n);arr.append(2**(lk+1))
        lk+=1
    
    
    
        
    for ps in range(3,ceil(sqrt(n))+1,2):
        lk=0
        cc=0
        while n%ps==0:
            n=n//ps
            #cc=1
            #arr.append(n);arr.append(ps**(lk+1))
            lk+=1
        
            
            
    if n!=1:
        #lk+=1
        #arr[n]=1
        #ans*=n;
        lk+=1
        return False
        #return arr
    
    #print(arr)
    
    return True


#count=0
#dp=[[0 for i in range(m)] for j in range(n)]
#[int(x) for x in input().strip().split()]
def gcd(x, y): 
      
    while(y): 
        x, y = y, x % y 
      
    return x 
          
# Driver Code         
def factorials(n,r):
    #This calculates ncr mod 10**9+7
    slr=n;dpr=r
    qlr=1;qs=1
    mod=10**9+7
    
    for ip in range(n-r+1,n+1):
        qlr=(qlr*ip)%mod
    for ij in range(1,r+1):
        qs=(qs*ij)%mod
    #print(qlr,qs)
    ans=(qlr*modInverse(qs))%mod
    return ans

        
        
def modInverse(b):
    qr=10**9+7
    return pow(b, qr - 2,qr)

#===============================================================================================
### START ITERATE RECURSION ###
from types import GeneratorType
def iterative(f, stack=[]):
  def wrapped_func(*args, **kwargs):
    if stack: return f(*args, **kwargs)
    to = f(*args, **kwargs)
    while True:
      if type(to) is GeneratorType:
        stack.append(to)
        to = next(to)
        continue
      stack.pop()
      if not stack: break
      to = stack[-1].send(to)
    return to
  return wrapped_func
def power(arr):
  listrep = arr
  subsets = []
  for i in range(2**len(listrep)):
    subset = []
    for k in range(len(listrep)):            
      if i & 1<<k:
        subset.append(listrep[k])
    subsets.append(subset)        
  return subsets
def pda(n) :
    list=[];su=0
    for i in range(1, int(sqrt(n) + 1)) :
         if (n % i == 0) :
            if (n // i == i) :
                list.append(i)
                su+=i
            else :
                list.append(n//i);list.append(i)
                su+=i;su+=n//i
    # The list will be printed in reverse    
    return su
def dis(xa,ya,xb,yb):
    return sqrt((xa-xb)**2+(ya-yb)**2)
#### END ITERATE RECURSION ####

 
#===============================================================================================
#----------Input functions--------------------#
def ii():
    return int(input())
def ilist():
    return [int(x) for x in input().strip().split()]
def islist():
    return list(map(str,input().split().rstrip()))
def inp():
    return input().strip()
def google(test,ans):
    return "Case #"+str(test)+": "+str(ans);
def overlap(x1,y1,x2,y2):
    if x2>y1:
        return y1-x2
    if y1>y2:
        return y2-x2
    return y1-x2;


###-------------------------CODE STARTS HERE--------------------------------###########

        
    

def dist(x1,y1,x2,y2):
    return sqrt((x1-x2)**2+(y1-y2)**2)
            
#########################################################################################
t=int(input())
#t=1
for p in range(t):
    #n,m=ilist()
    n,k=ilist()
    #arr=ilist()
    peak=ceil(n/2)-1
    if k>peak:
        print(-1)
        continue
    maxx=n
    ans=[0]*n
    i=1
    while k>0:
        ans[i]=maxx
        i+=2
        k-=1
        maxx-=1
        #print(i)
    mi=1
    for i in range(n):
        if ans[i]==0:
            ans[i]=mi
            mi+=1
    print(*ans)