I can't solve it:

You are given 8 integers:

• A, B, C representing a line on a plane with equation A*x + B*y = C
• a, b, c representing another line
• x, y representing a point on a plane

The two lines are not parallel therefore divide plane into 4 pieces. Point (x, y) lies inside of one these pieces.

Problem:
Write a fast algorithm that will find a point with integer coordinates in the same piece as (x,y) that is closest to the cross point of the two given lines.

Note:
This is not a homework, this is old Euler-type task that I have absolutely no idea how to approach.

Update: You can assume that the 8 numbers on input are 32-bit signed integers. But you cannot assume that the solution will be 32 bit.