You are given an array of length and you need to rearrange the array to satisfy that there exists at least one number that appears at least once in the array and for each pair that satisfy .

If there is no such array exist, please output . Otherwise, output the array rearranged with the minimum lexicographical order.

输入描述:

The first line contains one integer , denoting the number of test cases.

Each test case contains two lines.

The first line contains two integers  denoting the length of array  and the minimum distance defined in the statement above.

The second line contains  integers, the  integer  denotes the  number of array .

It is guaranteed that the sum of  in all test cases does not exceed .

输出描述:

For each test case output one line.

If there is no solution output  in one line, otherwise output  integers as the solution array with minimum lexicographical order.

4
4 3
1 2 1 2
4 4
1 1 2 2
6 3
3 3 2 2 1 1
7 3
1 1 2 2 2 3 3

1 2 2 1
-1
1 1 2 3 3 2
1 1 2 3 2 2 3