Problem H
Chugging
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Alice and Bob have challenged each other to finish as many bottles as quickly as they can, an activity known as chugging in North American slang.
It takes Alice $t_ A$ seconds to finish the first bottle. However, the bottle contents (gas, complex carbohydrates, alcohol) have deleterious effects on performance, so the second bottle takes her $t_ A+d_ A$ seconds to finish. This effect is cumulative: with every new bottle, Alice’s chugging speed deteriorates by $d_ A$ additional seconds.
For instance, if $t_ A=10$ and $d_ A=2$ as in the sample inputs below, then Alice needs
\[ 10 + (10 + 2) + (10 + 2 + 2)=36 \]seconds to finish $3$ bottles.
The corresponding values for Bob are $t_ B$ and $d_ B$.
Who finishes first?
Input
The input consists of three lines. The first line contains the number $N$ of bottles they each have to finish, with $1\leq N \leq 10$. The second line contains the integers $t_ A$ and $d_ A$, with $1\leq t_ A\leq 120$ and $0\leq d_ A\leq 120$. The third line contains the integers $t_ B$ and $d_ B$, with $1\leq t_ B\leq 120$ and $0\leq d_ B\leq 120$.
Output
Print “Alice” if Alice finishes first, or “Bob” if Bob finishes first. If they finish at the same time, print an equality symbol, “=”.
| Sample Input 1 | Sample Output 1 |
|---|---|
3 10 2 8 3 |
Bob |
| Sample Input 2 | Sample Output 2 |
|---|---|
3 10 2 8 4 |
= |
| Sample Input 3 | Sample Output 3 |
|---|---|
3 10 2 8 5 |
Alice |
| Sample Input 4 | Sample Output 4 |
|---|---|
2 1 1 1 0 |
Bob |
