Problem D
Time Travelling Temperatures
Hello from the future. I am a time traveller. You would think that in the future we have agreed to use a single scale for measuring temperature. This is not so. In fact, we have all sorts of scales now. All the big brands have made their own. This is a bit confusing. Please help me figure it out. In my day to day work I have to relate to two different scales $A$ and $B$. Help me find a temperature where the two scales are the same, so I don’t have to worry about it.
Input
Input consists of two space-separated integers, $X$ and $Y$. $X$ is the point on $B$ where $A$ is zero. $Y$ is the number of degrees in $B$ that equal a change of a single degree in $A$.
Output
Output the temperature where both scales are the same. This number must have an absolute or relative error of at most $10^{-6}$. If no such temperature exists, output “IMPOSSIBLE” (without the quotes) instead. If more than one such point exists, output “ALL GOOD” (without the quotes) instead.
Limits
-
$-100 \leq X \leq 100$
-
$1 \leq Y \leq 100$
| Sample Input 1 | Sample Output 1 |
|---|---|
32 2 |
-32 |
| Sample Input 2 | Sample Output 2 |
|---|---|
1 3 |
-0.500000000 |
