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 math
from collections import defaultdict
from sys import stdout

DEBUG = True

def log(*args, **kwargs):
    if DEBUG:
        print(*args, **kwargs)
 
def ri():
    return int(input())
 
def rl(f=int):
    return list(map(f, input().split()))
 
def rs():
    return input()
 
class Solution:
    
    def __init__(self):
        pass
        
    def run(self):

        n, k = rl()

        if (n % 2 == 0 and k > (n - 2) // 2) or (n % 2 == 1 and k > (n - 2 + 1) // 2):
            return -1

        result = [0] * n

        i = 1
        current = n
        while k > 0:
            result[i] = current
            i += 2
            current -= 1
            k -= 1

        current = 1
        for i in range(n):
            if result[i] == 0:
                result[i] = current
                current += 1

        return " ".join(map(str, result))

        
                        
if __name__ == '__main__':
    
    t = int(input())
    s = Solution()
    #s.run()
    #print(s.run())
    for i in range(t):
    #    s.run()
        print(s.run())