Two ants
Description
Two ants live at points $a_1$ and $a_2$ of the coordinate axis. At the same time and at a constant speed, they begin to run in a certain direction. The first ant knows that after $t_1$ seconds he will be at the point $p_1$. The second one knows that in $t_2$ seconds he will be at the point $p_2$. Determine if the ants will ever meet at the same point. If so, how soon will they meet?
The first line contains 3 integers $a_1$, $t_1$, $p_1$, $(-10^4 \leq a_1 \leq 10^4,$ $1 \leq t_1 \leq 10^4,$ $-10^4 \leq p_1 \leq 10^4,$ $a_1 \neq p_1)$. The second line contains 3 integers $a_2$, $t_2$, $p_2$, $(-10^4 \leq a_2 \leq 10^4,$ $1 \leq t_2 \leq 10^4,$ $-10^4 \leq p_2 \leq 10^4,$ $a_2 \neq p_2)$. Also $a_1 \neq a_2$.
Print -1 if the ants never meet. Otherwise, print a single number - the time until the meeting. It must differ from the correct answer by no more than $10^{-6}$.
Input
The first line contains 3 integers $a_1$, $t_1$, $p_1$, $(-10^4 \leq a_1 \leq 10^4,$ $1 \leq t_1 \leq 10^4,$ $-10^4 \leq p_1 \leq 10^4,$ $a_1 \neq p_1)$. The second line contains 3 integers $a_2$, $t_2$, $p_2$, $(-10^4 \leq a_2 \leq 10^4,$ $1 \leq t_2 \leq 10^4,$ $-10^4 \leq p_2 \leq 10^4,$ $a_2 \neq p_2)$. Also $a_1 \neq a_2$.
Output
Print -1 if the ants never meet. Otherwise, print a single number - the time until the meeting. It must differ from the correct answer by no more than $10^{-6}$.
-3 2 5
12 1 10
2.50000000