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>
using namespace std;
#define ll long long int
const ll mod = 1000000007;
int main()
{
  ll t;
  cin >> t;
  while(t--) {
      ll n, k;
      cin >> n >> k;
      vector<ll> a(n + 1);
      ll idx, x = 1;
      a[1] = x;
      x++;
      for(ll i = 2; i <= n; i++) {
          if(k > 0) {
              if((x + 1) <= n) {
                  a[i] = x + 1;
                  a[i + 1] = x;
                  i++;
                  x += 2;
                  k--;
              }
              else {
                  a[i] = x;
                  x++;
              }
          }
          else {
              a[i] = x;
              x++;
          }
      }
      if(k) {
          cout << -1 << endl;
      }
      else {
          for(ll i = 1; i <= n; i++) {
              cout << a[i] << " ";
          }
          cout << endl;
      }
  }
}