Problem D: Tour de FranceA 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 d1<d2 are adjacent if there is no other drive ratio d1<d3<d2. The spread between a pair of drive ratios d1<d2 is their quotient: d2/d1. You are to compute the maximum spread between two adjacent drive ratios achieved by a particular pair of front and rear clusters.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.
2 4 40 50 12 14 16 19 0
Output for Sample Input
Generate all of the possible ratios, then calculated the maximum.