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())
for j in range(t):
    m, n = map(int, input().split())
    h = n
    x = [0]*m
    if m>2:
        if m%2==1:
            if n>m//2:
                print(-1)
            else:
                i=1
                p=m
                while n>0:
                    x[i]=p
                    p-=1
                    n-=1
                    i+=2
                for i in range(0, m):
                    if x[i]==0:
                        x[i]=p
                        p-=1
                d = 0
                for y in range(1, m-1):
                    if x[y]>x[y+1] and x[y]>x[y-1]:
                        d+=1
                if d==h:
                    print(*x)
                else:
                    print(-2)
        else:
            if n>(m-1)//2:
                print(-1)
            else:
                i = 1
                p = m
                while n>0:
                    x[i]=p
                    p-=1
                    n-=1
                    i+=2
                for i in range(0, m):
                    if x[i]==0:
                        x[i]=p
                        p-=1
                d = 0
                for y in range(1, m-1):
                    if x[y]>x[y+1] and x[y]>x[y-1]:
                        d+=1
                if d==h:
                    print(*x)
                else:
                    print(-1)
    else:
        if m==1:
            if n==0:
                print(1)
            else:
                print(-1)
        else:
            if n==0:
                print(1, 2)
            else:
                print(-1)