Suppose you are in a 2-Dimensional world. Now, you are in a system of N parallel zones of same or different speed, numbered from 0 to N − 1. In each zone you can move in some given constant speed (Si amount per second in i-th zone) at any direction. Each zone is parallel to X axis, starting from the X axis (and then on the positive X and positive Y part only). Width of each zone is 100 (along the Y axis). You are currently in the origin (0, 0). You need to reach (100 ∗ N, D) coordinate. But, you want to do that in minimum possible time (seconds). Here is an example with N = 4, and D = 350. The arrows show a possible path from (0, 0) to (400, 350). Note that after the end of each zone (except the last one), it is possible that you may be in an non-integer ‘X’ coordinate. Given N, D, and the speeds S0, S1, S2, ..., SN−1 you will need to find the minimum possible time in seconds to reach the destination point. Input Input starts with an integer T (≤ 50), denoting the number of test cases. Each case contains two lines. In the first line you will be given two integers N (1 ≤ N ≤ 100) and D (0 ≤ D ≤ 10000). In the second line you will be given N integers, the speeds, in the order: S0, S1, S2,...,SN−1. Forall0≤i<N,1≤Si ≤1000. Output For each test case, generate one line of output, in the format ‘Case < case−no >: < answer >’. Here < case − no > is the case number starting from 1, and < answer > is the minimum possible time in
2/2 seconds. Your output should not differ more than 10−6 = 0.000001. You should print at least 8 digits after the decimal point for < answer >. Sample Input 2 10 50 3 400 10 10 10 Sample Output Case 1: 2.00000000 Case 2: 50.00000000