#CFRAC2. Continuous Fractions Again
Continuous Fractions Again
A simple continuous fraction has the form:
where the ai’s are integer numbers.
The previous continuous fraction could be noted as [a1, a2, . . . , an]. It is not difficult to show that any rational number p / q , with integers p > q > 0, can be represented in a unique way by a simple continuous fraction with n terms, such that p / q = [a1, a2, . . . , an−1, 1], where n and the ai’s are positive natural numbers.
Now given a simple continuous fraction, your task is to calculate a rational number which the continuous fraction most corresponds to it.
Input
Input for each case will consist of several lines. The first line is two integer m and n,which describe a char martrix,then followed m lines,each line cantain n chars. The char martrix describe a continuous fraction The continuous fraction is described by the following rules:
The end of the input is indicated by a line containing 0 0.
Output
Output will consist of a series of cases, each one in a line corresponding to the input case. A line describing a case contains p and q, two integer numbers separated by a space, and you can assume that 10^20 > p > q > 0.
Example
Input: 9 17 ..........1...... 2.+.------------- ............1.... ....4.+.--------- ..............1.. ........1.+.----- ................1 ............5.+.- ................1 5 10 ......1... 1.+.------ .........1 ....11.+.- .........1 0 0 Output: 75 34 13 12