E	Speed Zones

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 (S_i 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, ..., S_N-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, ..., S_N-1. For all 0≤ i < N , 1 ≤ S_i ≤ 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 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	Output for Sample Input
2 1 0 50 3 400 10 10 10	Case 1: 2.00000000 Case 2: 50.00000000

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Problem Setter: Shahriar Rouf Nafi, Special Thanks: Tanaeem M Moosa