I. Inventory
time limit per test
10.0 s
memory limit per test
256 megabytes
input
standard input
output
standard output

Fish was retired from programming, and now he goes back home and runs a shop.

There are $$$N$$$ kinds of goods in sale in his shop, and the $$$i$$$-th goods will be sold exactly $$$x_i$$$ pieces everyday. However, as his inventory shelf has a fixed and limited volume $$$V$$$, he has to manage the distribution of these goods. To do so, he wants to assign a real value $$$v_i$$$ to $$$i$$$-th goods as its maximum quantity storing in the shelf such that $$$\sum v_i = V$$$. When one kind of goods is sold out, he can refill the shelf with this goods to its maximum quantity. As a result, for $$$i$$$-th goods, he will refill $$$\dfrac{x_i }{ v_i}$$$ times per day.

Please help Fish determine the $$$v_i$$$ for all goods so that the number of times he use to refill all the goods everyday is minimum.

Input

The first line of input contains an integer $$$T$$$, representing the number of test cases.

Then for each test case:

The first line contains two integers $$$N, V$$$ as mentioned above.

The second line contains $$$N$$$ integers $$$x_1,x_2,\cdots,x_N$$$ as mentioned above.

All numbers in the same line are separated by one space.

Output

For each test case, you should output Case $$$x$$$: $$$y$$$, where $$$x$$$ indicates the case number starting from $$$1$$$, and $$$y$$$ is the minimum number of times he refills the goods of all kinds in one day.

Your answer will be considered correct if its absolute error does not exceed $$$10^{-6}$$$.

Example
Input
2
2 2
1 1
2 2
2 8
Output
Case 1: 2.000000
Case 2: 9.000000
Note

$$$1 \le T \le 100$$$

$$$1 \le N \le 10^5$$$

$$$1 \le V \le 10^9$$$

For $$$90\%$$$ test cases: $$$N \le 100$$$