John's Sorting of Binary Strings

You are given n binary strings, each of fixed width k. Your task is to sort these binary strings based on their first p bits.

Formally, for each binary string s, consider its prefix of length p (i.e. the first p characters of s). The sorting should be done in lexicographical order of these prefixes. In other words, given two strings \(s_1\) and \(s_2\), they are compared based on the value of \(s_1[0:p]\) and \(s_2[0:p]\), where the notation represents the substring from index 0 (inclusive) to \(p\) (exclusive).

It is guaranteed that all the binary strings are exactly of length k and consist only of the characters '0' and '1'.

inputFormat

The input is read from standard input (stdin) and has the following format:

 n k p
 s1
 s2
 ...
 sn

Where:

• n is the number of binary strings.
• k is the fixed width (length) of each binary string.
• p is the number of bits from the beginning of each string that are used to determine the sorting order.
• s1, s2, ..., sn are the binary strings.

outputFormat

Output the sorted list of binary strings to standard output (stdout). Each binary string should be printed on a new line, in the order determined by sorting based on its first p bits.

## sample

3 5 3
11010
10100
11100

10100
11010
11100

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