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:
from sys import *
'''sys.stdin = open('input.txt', 'r')  
sys.stdout = open('output.txt', 'w') '''
from collections import defaultdict as dd
from math import *
from bisect import *
#sys.setrecursionlimit(10 ** 8)
def sinp():
    return input()
def inp():
    return int(sinp())
def minp():
    return map(int, sinp().split())
def linp():
    return list(minp())
def strl():
    return list(sinp())
def pr(x):
    print(x)
mod = int(1e9+7)
for _ in range(inp()):
    n, k = minp()
    if 2 * k + 1 > n:
        pr(-1)
    else:
        l = []
        m = n - (2 * k + 1) - 1
        a = k + 1
        b = a + 1
        for i in range(a):
            l.extend([a, b])
            a -= 1
            b += 1
        if m == -1:
            print(*l[:-1])
        else:
            l.extend([i for i in range(b, b + m)])
            print(*l)