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