Today is your birthday and you invite $k$ friends.
You have $n$ squared cakes and they all have the height $1$. The $i^{th}$ cake have an edge length of $A_i$.
Now you want to cut these cakes in such a way that each friend has the same amount of cake, and each piece of cake must be cut from **at most** 1 cake (i.e. you can't cut a a piece of cake of size $a$ from cake $A$ and a piece of size $b$ from cake $B$ to make a piece of size $a + b$).
Find the maximum cake size your friends will receive.
### Input
- The first line contains 2 integers $n, k$.
- The second line contains $n$ integers $A_i$.
### Output
- Print the maximum size. Your answer will be considered correct if its absolute or relative error does not exceed $10^{-3}$. In other words, your answer, $x$, will be compared to the correct answer, $y$. If $|x-y| < 10^{-3}$, then your answer will be considered correct.
### Constraints
- $1 \le n, A_i \le 10^5$.
- $1 \le k \le 10^9$.
### Example
Input:
```
2 5
4 5
```
Output:
```
8.000
```
