Problem from the Regional ACM Contest.

## Problem B

Rational Numbers from Repeating Fractions

A
rational number is any which can be written in the form p/q, where p and q are
integers. All rational numbers less than 1 (that is, those for which p is less
than q) can be expanded into a decimal fraction, but this expansion may require
repetition of some number of trailing digits. For example, the rational number
7/22 has the decimal expansion .3181818.. Note that the pair of digits 1 and 8
repeat ad infinitum. Numbers with such repeating decimal expansions are usually
written with a horizontal bar over the repeated digits, like this:
If we are given the decimal expansion of a rational fraction (with an
indication of which digits are repeated, if necessary), we can determine the
rational fraction (that is, the integer values of p and q in p/q) using the
following algorithm.

Assume there are k digits immediately after the decimal point that are not
repeated, followed by a group of j digits which must be repeated. Thus for 7/22
we would have k = 1 (for the digit 3) and j = 2 (for the digits 1 and 8). Now if
we let X be the original number (7/22), we can compute the numerator and
denominator of the expression:

For
we obtain the following calculation for the numerator of this fraction:
The
denominator is just 1000 - 10, or 990. It is important to note that the
expression in the numerator and the denominator of this expression will always
yield integer values, and these represent the numerator and denominator of the
rational number. Thus the repeated fraction
is the decimal expansion of the rational number 315/990. Properly reduced, this
fraction is (as expected) just 7/22.
The input data for this problem will be a sequence of test cases, each test
case appearing on a line by itself, followed by a -1. Each test case will begin
with an integer giving the value of j, one or more spaces, then the decimal
expansion of a fraction given in the form 0.ddddd (where d represents a decimal
digit). There may be as many as nine (9) digits in the decimal expansion (that
is, the value of k+j may be as large as 9). For each test case, display the case
number (they are numbered sequentially starting with 1) and the resulting
rational number in the form p/q, properly reduced.

Sample Input

2 0.318
1 0.3
2 0.09
6 0.714285
-1

### Expected Output

Case 1: 7/22
Case 2: 1/3
Case 3: 1/11
Case 4: 5/7