J. Bouquet of Flowers
time limit per test
2.5 s
memory limit per test
256 megabytes
input
standard input
output
standard output

As a caring boyfriend, it's nice to give your girlfriend flowers along with gifts. So, you decide to get the prettiest bouquet of flowers within your budget, with the highest beauty score. The dream situation is to buy all the flowers in the shop: all $$$100$$$ available flowers from each type.

The person selling flowers is friendly, so he allowed you to buy any flower with $$$1$$$ dinar no matter its type.

The bouquet beauty score, $$$Beauty$$$, is a real number $$$(0\leq Beauty \leq 100)$$$ , showing how pretty the bouquet is out of $$$100$$$. The $$$Beauty$$$ of a bouquet is defined as the sum of the beauties of the flowers in that bouquet, divided by the sum of the beauties of each possible type of flowers.

So you decided to get the bouquet with the maximum possible beauty.

Input

In the first line, you are given the number of test cases $$$t$$$ $$$(1\leq t \leq 10)$$$.

For each test case, you're given in the first line two integers: $$$n$$$ and $$$c$$$, the number of types of flowers, your budget in dinars respectively. $$$(1\leq n \leq 5.10^{4})$$$ $$$(1\leq c \leq 10^{9})$$$.

In the second line, you get an array $$$a$$$ with $$$n$$$ real numbers, where $$$a_{i}$$$ ($$$1 \leq i \leq n$$$) representing the beauty coefficient for the $$$ith$$$ type of flower. $$$(1\leq a_{i} \leq 100)$$$.

Output

For each testcase, output the maximum possible beauty in separate lines. The answer should have a relative error less than $$$10^{-6}$$$.

Examples
Input
1
3 370
4 3 2
Output
100.000000000000000
Input
1
1 30
9
Output
30.000000000000000
Input
1
3 140
2 3 2
Output
54.285714285714285
Note

NB: You can't buy more than 100 flowers from the same type, as it is the number of available flowers from each type in each testcase.