CFRAC2 - Continuous Fractions Again


A simple continuous fraction has the form:

subir imagenes

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 matrix, then followed m lines, each line cantain n chars. The char matrix describe a continuous fraction The continuous fraction is described by the following rules:

  • Horizontal bars are formed by sequences of dashes '-'.
  • The width of each horizontal bar is exactly equal to the width of the denominator under it.
  • Blank characters should be printed using periods '.'
  • The number on a fraction numerator must be printed center justified. That is, the number of spaces at either side must be same, if possible; in other case, one more space must be added at the right side.

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

hide comments
hamza007: 2012-06-23 14:04:27

The continued fractions are also pretty large ... int wont suffice , Unsigned ll is to be used for them too .. This costed be several WAs ..

Sangha: 2012-02-02 16:03:34

i am getting WA again and again ........ please mention some test cases !!!!!!!

VinyleEm: 2011-01-20 06:49:24

Its possible to get AC just using long longs. So, don't worry about overflows.

[Trichromatic] XilinX: 2009-03-21 11:35:52

After solving this problem you may try problem CFRAC & ACFRAC.


Added by:Camilo Andrés Varela León
Date:2007-01-31
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:HNU Contest