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1043 - Triangle Partitioning

You are given ABAC and BCDE is parallel to BC. You are also given the area ratio between ADE and BDEC. You have to find the value of AD.See the picture below.


Input starts with an integer T (≤ 25), denoting the number of test cases.

Each case begins with four real numbers denoting AB, AC, BC and the ratio of ADE and BDEC (ADE / BDEC). You can safely assume that the given triangle is a valid triangle with positive area.


For each case of input you have to print the case number and AD. Errors less than 10-6 will be ignored.

Sample Input

Output for Sample Input

4100 100 100 210 12 14 17 8 9 10

8.134 9.098 7.123 5.10

Case 1: 81.6496580Case 2: 7.07106781Case 3: 6.6742381247Case 4: 7.437454786