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:


 
'''
Author : Shubhanshu Jain;
'''
 
import math
import random;
from collections import * 
mod =1000000007
r1 = lambda : int(input());
rm = lambda : map(int,input().split());
rms = lambda : map(str,input().split());
rls = lambda : list(rm())
 
def solve():
    test = r1();
    while(test):
        test-=1;
        n, k = rm();
        if(((n-1)//2)>=k):
            ls = [0]*n;
            i = 0;
            c = 0;
            x = 0;
            while(i<n):
                if(i%2 and c<k):
                    c+=1;
                else:
                    ls[i] = x+1;
                    x+=1;
                i+=1;
            i = 1;
            while(k):
                k-=1;
                ls[i] = n;
                i+=2;
                n-=1;
                
            print(*ls)
        else:
            print(-1);
            

def def_value(): 
	return "nan"
	
solve();