Declining Sequences [B]

Memory limit: 32 MB

Consider an integer sequence . A (strictly) increasing sequence of indices , where , is called declining if .

A sequence of indices is lexicographically smaller od than a sequence of indices if for some it holds that for each and .

Your task is to answer several queries of the form: find the (lexicographically) -th smallest declining sequence of indices.

Input

The first line of the standard input contains three integers , and (, ) that denote the length of the sequence , the length of the considered declining sequences and the number of queries. The second line contains integers (). The following lines contain descriptions of the queries: the -th of these lines contains a single integer ().

Output

Your program should write lines to the standard output. The -th line should contain the -th smallest declining sequence of indices or a single number if the requested declining sequence does not exist.

Example

For the input data:

5 3 3
-1 6 5 2 1
1
5
3

the correct result is:

2 3 4 
-1
2 4 5

Explanation of the example: The declining sequences of indices of length 3 in this example are, in the lexicographical order, as follows: , , and .

Task author: Adam Karczmarz.