8404번 - Straight Lines 다국어

We are given six integers: A₁, B₁, C₁, A₂, B₂, C₂ such that A₁B₂ ≠ A₂B₁. These numbers are coefficients in equations of two intersecting lines:

• l₁: A₁x + B₁y + C₁ = 0,
• l₂: A₂x + B₂y + C₂ = 0.

The lines divide the plane into four parts. We represent each part by any point with integer coordinates, belonging to this part (but not belonging to any of the lines l₁, l₂). You are given a point (a, b) with integer coordinates representing one part. Find a point with integer coordinates (c, d) representing the same part, such that its distance from the point of intersection of lines l₁ and l₂ is least possible.

Write a program which:

• reads the equations of lines l₁ and l₂ 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 l₁ and l₂,
• writes the answer to the standard output.

The first line of the standard input contains three numbers A₁, B₁, C₁, separated by single spaces - the coefficients of l₁'s equation. The second line contains three numbers A₂, B₂, C₂, separated by single spaces - the coefficients of l₂'s equation. It is true that A₁B₂ ≠ A₂B_!. The third and last line contains two integers a, b, separated by a single space. They are the coordinates of a point representing one part of plane. Point (a, b) does not belong to any of lines l₁, l₂. For every number x from the input it is true that -2 100 000 000 < x < 2 100 000 000.

Your program should write to the standard output two numbers c, d, separated by a single space - the coordinates of a point (c, d) representing the given part, closest to the point of intersection of lines l₁ and l₂. If there are many such points, your program should output only one of them.