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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 .