Little Tom likes amusing mathematical tasks a lot. After studying ordinary periodical
numbers he wondered, what if period will be before decimal point. Generally speaking,
such a "number" will have infinite number of digits before decimal point, and it will
not be even a number, but it is possible to apply some operations to them. But after
trying to sum up this numbers for a while, he found this task a bit complicated, even
when numbers have periods of the same length and don't have unperiodical part. So he decided
to write a program that will solve this problem. But he is not very good at programming,
so asked you to help him and write it.
Periodical numbers can be written in form
(a1a2…ak)b1b2…bm = …a1a2…ak a1a2…ak a1a2…ak b1b2…bm,
where ai and bj are digits. The summation process
starts from the less significant digit and going on like in addition of normal numbers,
but never finishes. Your task is to sum up two periodical infinite numbers.
Input has two lines containing two infinite periodical numbers each.
It is guaranteed that the given numbers will not have unperiodical part
(i.e. will be given in form "(a1a2 … ak)") and the given periods of
numbers will be the same length not greater than nine.
The output must have one line containing desired number itself. It must be
printed in the representation with minimal period length. Among such
representations the one having the least unperiodical part's length must
Problem Source: Novosibirsk SU Contest. Petrozavodsk training camp, September 2007