Tour de France

<p> 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 d₁&lt;d₂ are adjacent if there is no other drive ratio d₁&lt;d₃&lt;d₂. The <i>spread</i> between a pair of drive ratios d₁&lt;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. </p> <p> Input consists of several test cases, followed by a line containing 0. Each test case is specified by the following input: </p> <ul> <li> f: the number of sprockets in the front cluster; </li> <li> r: the number of sprockets in the rear cluster; </li> <li> f integers, each giving the number of teeth on one of the gears in the front cluster; </li> <li> r integers, each giving the number of teeth on one of the gears in the rear cluster. </li> </ul> <p> You may assume that no cluster has more than 10 sprockets and that no gear has fewer than 10 or more than 100 teeth. </p> <p> For each test case, output the maximum spread rounded to two decimal places. </p>

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