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 JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Solution1513A {
  public static void main(String[] args) {
    InputReader in = new InputReader(System.in);
    PrintWriter out = new PrintWriter(System.out);
    Solver1513A solver = new Solver1513A();
    int n = in.nextInt();
    for (int i = 0; i < n; i++) {
      solver.solve(i, in, out);
    }
    out.close();
  }

  static class Solver1513A {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
      int n = in.nextInt(), k = in.nextInt();

      if (k <= (n - 1) / 2) {
        int[] res = new int[n];

        for (int i = 0; i < k; i++) {
          res[i * 2 + 1] = n - i;
        }

        int next = n - k;
        for (int i = 0; i < n; i++) {
          if (res[i] == 0) {
            res[i] = next;
            next--;
          }
        }

        for (int i = 0; i < n; i++) {
          if (i > 0) {
            out.print(" ");
          }
          out.print(res[i]);
        }
        out.println();
      } else {
        out.println(-1);
      }
    }
  }

  static class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
      reader = new BufferedReader(new InputStreamReader(stream), 32768);
      tokenizer = null;
    }

    public String next() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.nextToken();
    }

    public int nextInt() {
      return Integer.parseInt(next());
    }
  }
}