Life can be taught, but sometimes simple problems are just very well hidden among
difficult ones. Once identifying those simple problems you are almost on a half way of solving
them as well as making one big step towards winning the contest. Just be careful, this is NOT the
simplest problem!
Are you ready for that challenge?
Your task is to write a program that transforms numbers from various numeric systems to
decade one (base=10).
Input file consists from multiple data sets separated by one or more empty lines.
First line of each set contains definition of digit ordering for some hypothetical numerical
system. All ASCII printable characters (codes greater than 0x20 (space)) are allowed to appear
as digits, and they are sorted according to increased decimal value (starting from zero).
Each line of the input data set (starting from second one) is one number coded with
previously defined digits. Such numbers can have multiple decade interpretations (taking different
base for hypothetical system) and your task is to find sum of all possible interpretations.
Explanation: If we define digit ordering as “0123456789” possible bases are 2..10 but
number “6201” can be decoded only in systems with base 7..10.
Input
Input lines can contain white space characters on both ends which should be ignored.
You are required to output one decimal number per each number from input data sets.
That number represents sum of decimal representations for all valid numeric system bases.
Output
Output data sets should be separated by one blank line.
Sample Input
0123456789
90763
1
.1>C
CC.
>.1
1....
Sample Output
90763
9
60
52
353
Hint
Source
Southeastern European Regional Programming Contest
Bucharest, Romania
October 27, 2007