Finding Suspicious Proteins

Little Claire studies proteins, which are sequences of amino acids. There are 20 amino acids
from which proteins are built. While amino acids all have proper names, such as alanine
or glycine, they are often denoted by single letters, so that proteins can be seen as
sequences of different lengths, such as 
DTASDAAAAAALTAABAAAAAKLTABBAAAAAAATAA,
TIFLQQQQQQQQQQQ
or even maybe RICKRQLL.

Comparing two proteins can be difficult, because they may contain active sites, which determine
their function in a cell, and less important parts of the sequence. Recent advances
in artificial neural networks made it possible to train a network that, given a protein, outputs
a sequence of  numbers, where each number roughly corresponds to a feature of a protein that
correlates with its possible functions in a cell. Such a sequence is called an embedding.

Claire is particularly interested in suspicious proteins, those which are really different
from others. For this purpose, she considers the so-called Manhattan distance between 
embeddings of proteins. For two protein embeddings  and  of length ,
the distance  is computed as follows:
equation*
    D(p, q) = _i=1^l p_i - q_i,
equation*
where  is the -th element of the embedding .

Claire wants to find  suspicious proteins in the given list of  proteins.
As a baseline for her studies, Claire wants to use the following greedy algorithm:
itemize
    Find a protein  which is the most distant from the first protein in the list.
    The second protein, , is chosen as the most distant protein from .
    The third one, , is chosen so that
          
          is maximum possible. That is, it must be far away from both previously chosen proteins.
    All subsequent proteins , , are chosen in a similar way: the minimum of
          the distances to all the previously chosen proteins should be maximum possible.
itemize
Note that, in the case of ties, the first matching protein in the list must be chosen.

Claire's implementation works nicely for small numbers  and , but becomes too slow as they increase.
You must find a way to optimise this.

Input

The first line contains three numbers  ,  
and  : the overall number of proteins,
the length of each protein embedding, and the number of proteins to choose.

Each of the following  lines starts with a protein identifier, which is a sequence
of at least one and most ten capital letters and/or numbers. Then, separated by whitespace,
come  single-digit integer numbers  (), which
define the embedding of the protein.
All protein identifiers will be different.

Output

Output the identifiers of  chosen proteins, one per line,
in their respective order ( to ).
