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Zadanie Proste (pro)
Straight Lines
Memory limit: 32 MB
We are given six integers: 
, 
, 
, 
,
, 
such that 
.
These numbers are coefficients in equations of two intersecting lines:
-
,
-
.
, 
).
You are given a point 
with integer coordinates representing one part. Find a point with integer coordinates 
representing the same part, such that its distance from the point of intersection
of lines 
and 
is least possible.
Task
Write a program which:
-
reads the equations of lines
and 
and a point
representing one part of plane,
-
finds a point with integer coordinates representing the given part
and closest to the point of intersection of lines
and 
,
- writes the answer to the standard output.
Input
The first line of the standard input contains three numbers
, separated by single spaces -
the coefficients of 
's equation.
The second line contains three numbers 
, separated by single spaces -
the coefficients of 
's equation.
It is true that 
.
The third and last line contains two integers 
,
separated by a single space. They are the coordinates of a point
representing one part of plane.
Point 
does not belong to any of lines 
, 
.
For every number 
from the input it is true that
.
Output
Your program should write to the standard output two numbers
, separated by a single space - the coordinates of a point
representing the given part, closest to the point of
intersection of lines 
and 
.
If there are many such points, your program should output only
one of them.
Example
For the input data:
1 -1 1 2 -3 1 5 4
the correct result is:
2 2
Task author: Jakub Pawlewicz.