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:
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
#define db long double
#define ll long long int
#define el '\n'
#define pb push_back
#define mp make_pair
#define IOS ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define F first
#define S second
#define debug(x) cout << "[" << #x  << " : " << x << " ]" << endl;
#define print(x) cout << x << endl;
#define MAXN 1000000007 //10^9+7
typedef pair<ll, ll> pi;
typedef vector<pi> vpii;
typedef vector<ll> vi;
typedef vector<vector<ll>> vvii;
typedef map<db, db> MAP;
void printset(multiset<ll> s)
{
	multiset<ll>::iterator itr = s.begin();
	for (itr; itr != s.end(); itr++)
		cout << *(itr) << " ";
	cout << el;
}
void no()
{
	cout << -1 << el;
}
int main()
{
#ifndef ONLINE_JUDGE
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
#endif
	IOS
	ll t;
	cin >> t;
	for (ll q = 1; q <= t; ++q)
	{
		ll n;
		cin >> n;
		ll k;
		cin >> k;
		if (2 * k + 1 > n)
			cout << -1 << el;
		else
		{
			ll v[n];
			for (int i = 0; i <= n - 1; ++i)
			{
				v[i] = i + 1;
			}
			ll i = 1;
			while (k > 0 and i < n)
			{
				swap(v[i], v[i + 1]);
				i += 2;
				k--;
			}
			if (k == 0)
			{
				for (int i = 0; i < n; ++i)
				{
					/* code */
					cout << v[i] << " ";
				}
				cout << el;
			}
			else
			{
				cout << -1 << el;
			}
		}
	}
}