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Fibinary Numbers
The standard interpretation of the binary number 1010 is 8 + 2 = 10. An alternate way to
view the sequence ``1010'' is to use Fibonacci numbers as bases instead of powers of two.
For this problem, the terms of the Fibonacci sequence are:
| Fibinary Numbers |
Where each term is the sum of the two preceding terms (note that there is only one 1 in
the sequence as defined here). Using this scheme, the sequence ``1010'' could be
interpreted as
.
This
representation is called a Fibinary number.
Note that there is not always a unique Fibinary representation of every number. For
example the number 10 could be represented as either 8 + 2 (10010) or as 5 + 3 + 2
(1110). To make the Fibinary representations unique, larger Fibonacci terms must
always be used whenever possible (i.e. disallow 2 adjacent 1's). Applying this rule to the
number 10, means that 10 would be represented as 8+2 (10010).
Input and Output
Write a program that takes two valid Fibinary numbers and prints the sum in Fibinary form. These numbers will have at most 100 digits.In case that two or more test cases had to be solved, it must be a blank line between two consecutive, both in input and output files.
Sample Input
10010 1 10000 1000 10000 10000
Sample Output
10100 100000 100100
Miguel Revilla
2000-12-30