Problem D
Tour de France
A racing bicycle is driven by a chain connecting two sprockets. Sprockets are grouped into two clusters: the front cluster (typically consisting of 2 or 3 sprockets) and the rear cluster (typically consisting of between 5 and 10 sprockets). At any time the chain connects one of the front sprockets to one of the rear sprockets. The drive ratio – the ratio of the angular velocity of the pedals to that of the wheels – is $n/m$ where $n$ is the number of teeth on the rear sprocket and $m$ is the number of teeth on the front sprocket. Two drive ratios $d_1 < d_2$ are adjacent if there is no other drive ratio $d_1 < d_3 < d_2$. The spread between a pair of drive ratios $d_1 < d_2$ is their quotient: $d_2/d_1$. You are to compute the maximum spread between two adjacent drive ratios achieved by a particular pair of front and rear clusters.
Input
Input consists of several test cases, followed by a line containing 0. Each test case is specified by the following input:
-
$f$: the number of sprockets in the front cluster;
-
$r$: the number of sprockets in the rear cluster;
-
$f$ integers, each giving the number of teeth on one of the gears in the front cluster;
-
$r$ integers, each giving the number of teeth on one of the gears in the rear cluster.
You may assume that no cluster has more than $10$ sprockets and that no gear has fewer than $10$ or more than $100$ teeth.
Output
For each test case, output the maximum spread rounded to two decimal places.
| Sample Input 1 | Sample Output 1 |
|---|---|
2 4 40 50 12 14 16 19 0 |
1.19 |
