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 CPP):

Solution:
#include <bits/stdc++.h>
 
#define ios ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define file(s) if (fopen(s".in", "r")) freopen(s".in", "r", stdin), freopen(s".out", "w", stdout)
#define all(a) a.begin() , a.end()
#define F first
#define S second
 
using namespace std;
using ll = long long;
 
const int N = 2e5+5 , inf = 2e9 + 7;
const ll INF = 1e18 ,   mod = 1e9+7 , P = 6547;

int a[N];

void solve() {
	int n , k;
	cin >> n >> k;
	for(int i = 1; i <= n; i ++) a[i] = 0;
	for(int i = 2 , x = n; i < n && k > 0; i += 2) {
		a[i] = x--;
		k --;	
	}
	if(k > 0) {
		cout << -1 << '\n';
		return;
	}
	for(int i = 1 , x = 1; i <= n; i ++) {
		if(a[i] == 0) a[i] = x++;
		cout << a[i] << ' ';
	}
	cout << '\n';
}
/*
*/
int main() {
    ios;
    int tt = 1;
    cin >> tt;
    while(tt --) {
        solve();
    }
    return 0;
}