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.*;
import java.lang.*;
import java.util.*;

public class A1513 {
    public static void main(String[] args) throws IOException{
        StringBuffer ans = new StringBuffer();
        StringTokenizer st;
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        st = new StringTokenizer(f.readLine());
        int t = Integer.parseInt(st.nextToken());
        for(; t > 0; t--){
            st = new StringTokenizer(f.readLine());
            int n = Integer.parseInt(st.nextToken());
            int k = Integer.parseInt(st.nextToken());
            Deque<Integer> deque = new Deque<Integer>() {
                @Override
                public void addFirst(Integer integer) {

                }

                @Override
                public void addLast(Integer integer) {

                }

                @Override
                public boolean offerFirst(Integer integer) {
                    return false;
                }

                @Override
                public boolean offerLast(Integer integer) {
                    return false;
                }

                @Override
                public Integer removeFirst() {
                    return null;
                }

                @Override
                public Integer removeLast() {
                    return null;
                }

                @Override
                public Integer pollFirst() {
                    return null;
                }

                @Override
                public Integer pollLast() {
                    return null;
                }

                @Override
                public Integer getFirst() {
                    return null;
                }

                @Override
                public Integer getLast() {
                    return null;
                }

                @Override
                public Integer peekFirst() {
                    return null;
                }

                @Override
                public Integer peekLast() {
                    return null;
                }

                @Override
                public boolean removeFirstOccurrence(Object o) {
                    return false;
                }

                @Override
                public boolean removeLastOccurrence(Object o) {
                    return false;
                }

                @Override
                public boolean add(Integer integer) {
                    return false;
                }

                @Override
                public boolean offer(Integer integer) {
                    return false;
                }

                @Override
                public Integer remove() {
                    return null;
                }

                @Override
                public Integer poll() {
                    return null;
                }

                @Override
                public Integer element() {
                    return null;
                }

                @Override
                public Integer peek() {
                    return null;
                }

                @Override
                public boolean addAll(Collection<? extends Integer> c) {
                    return false;
                }

                @Override
                public void push(Integer integer) {

                }

                @Override
                public Integer pop() {
                    return null;
                }

                @Override
                public boolean remove(Object o) {
                    return false;
                }

                @Override
                public boolean contains(Object o) {
                    return false;
                }

                @Override
                public int size() {
                    return 0;
                }

                @Override
                public Iterator<Integer> iterator() {
                    return null;
                }

                @Override
                public Iterator<Integer> descendingIterator() {
                    return null;
                }

                @Override
                public boolean isEmpty() {
                    return false;
                }

                @Override
                public Object[] toArray() {
                    return new Object[0];
                }

                @Override
                public <T> T[] toArray(T[] a) {
                    return null;
                }

                @Override
                public boolean containsAll(Collection<?> c) {
                    return false;
                }

                @Override
                public boolean removeAll(Collection<?> c) {
                    return false;
                }

                @Override
                public boolean retainAll(Collection<?> c) {
                    return false;
                }

                @Override
                public void clear() {

                }
            };
            int[] arr = new int[n];
            for(int i = 0; i < n; i++)
                deque.add(i+1);
            //System.out.println(deque);
            int peaks = 0;
            int ft = 1;
            int sc = n;
            for(int i = 0; i < n; i++){
                if(i % 2 == 0 || peaks == k){
                    arr[i] = ft;
                    ft++;
                }else{
                    arr[i] = sc;
                    sc--;
                    peaks++;
                }
            }
            peaks = 0;
            for(int i = 1; i < n-1; i++){
                if(arr[i] > arr[i-1] && arr[i] > arr[i+1]){
                    peaks++;
                }
            }
            //System.out.println(Arrays.toString(arr));
            if(peaks == k){
                for(int i : arr){
                    ans.append(i).append(" ");
                }
            }else
                ans.append("-1");
            ans.append("\n");
        }
        f.close();



        System.out.println(ans);
    }

}