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 CY cout<<"YES\n"
#define CN cout<<"NO\n"
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const int inf=0x3f3f3f3f;
const ll INF=0x3f3f3f3f3f3f3f3f;
const int MAXN=2e5+10;
const int N=1002;
const ll mod=1e9+7;
inline int read()
{
    int x=0,f=1;char ch=getchar();
    while (!isdigit(ch)){if (ch=='-') f=-1;ch=getchar();}
    while (isdigit(ch)){x=x*10+ch-48;ch=getchar();}
    return x*f;
}
int a[N];
int main(){
	ios::sync_with_stdio(false);
	int T;cin>>T;
	while(T--){
		int n,k;cin>>n>>k;
		int t=n/2;
		if(n%2==0) --t;
		if(k>t){
			cout<<"-1\n";
			continue;
		}
		int cnt=0;
		for(int i=1;i<=n;++i) a[i]=i;
		for(int i=2;cnt<k;i+=2){
			swap(a[i],a[i+1]);
			++cnt;
		}
		for(int i=1;i<=n;++i) cout<<a[i]<<' ';
		cout<<'\n';
	}
}