Numerals of the Przesmyks

A tribe called the Przesmyks wrote natural numbers using only two symbols, - and +. Every legal numeral is a non-empty string of these two symbols that obeys a single rule: no more than $m$ - symbols may appear in a row. The bound $m$ changed from year to year and always lay between 1 and 113.

Once the bound $m$ is fixed, all legal strings are ordered first by length (shorter strings first) and then, among strings of equal length, alphabetically, where - comes before +. Listed in this order, the strings represent the successive numbers 0, 1, 2, ….

For example, when at most one - in a row is allowed ($m = 1$), the numerals begin like this:

When the bound changes, the way a number is written changes too. For instance, if two or more - in a row are allowed, the number 2 is written as --.

Write a program that reads two bounds and a list of numbers written under the first bound, and rewrites each of them under the second bound.

The first line contains three integers $m_1$, $m_2$ and $n$ separated by single spaces, where $1 \le m_1, m_2 \le 113$ and $1 \le n \le 10$. Here $m_1$ is the bound on the maximum number of consecutive - symbols in the input numerals, and $m_2$ is the bound for the numerals that must be written out. $n$ is the number of numerals to convert.

Each of the next $n$ lines contains one numeral, a string of - and +. No numeral is longer than 1000 characters.

Print $n$ lines. On each line print the corresponding input number rewritten under the bound $m_2$.