Straight Lines

You are given six integers $A_1, B_1, C_1, A_2, B_2, C_2$ with $A_1 B_2 \neq A_2 B_1$. They are the coefficients of two lines that cross at a single point:

• $l_1: A_1 x + B_1 y + C_1 = 0$
• $l_2: A_2 x + B_2 y + C_2 = 0$

These two lines divide the plane into four regions. Each region can be named by any integer point that lies inside it, that is, a point lying on neither line. You are given one such integer point $(a, b)$. Among all integer points that lie in the same region as $(a, b)$, find the one whose Euclidean distance to the intersection point of $l_1$ and $l_2$ is smallest.

The first line contains three integers $A_1, B_1, C_1$ separated by single spaces, the coefficients of $l_1$. The second line contains three integers $A_2, B_2, C_2$, the coefficients of $l_2$; it is guaranteed that $A_1 B_2 \neq A_2 B_1$. The third line contains two integers $a$ and $b$, the coordinates of a point that lies in one region and on neither line. Every integer $x$ in the input satisfies $-2100000000 < x < 2100000000$.

Print two integers $c$ and $d$ separated by one space: the coordinates of an integer point that lies in the same region as $(a, b)$ and whose distance to the intersection of $l_1$ and $l_2$ is as small as possible. If several integer points share that smallest distance, print the lexicographically smallest one: the point with the smallest $c$, and among those the one with the smallest $d$.

The two lines split the plane into four regions, and the point $(a, b)$ selects one of them. The answer is the integer point of that region closest to the crossing point.