C. Testing Subjects Usually Die
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Hello, and again, welcome to the Aperture Science Enrichment Center.

You wake up in an unfamiliar room and a robotic voice greets you. You're in trouble.

The voice explains that you're being a subject of an ethically questionable series of experiments. The test you're undergoing right now goes as follows. An AI picked an integer number from $$$1$$$ to $$$n$$$ in such a way that the number $$$k$$$ had a probability $$$\frac{p_k}{p_1+\dots+p_n}$$$ to be picked. You need to guess the number.

If you guess it incorrectly, you'll be put to sleep, your memory will be erased and you will undergo the same test again. With a probability of $$$c$$$ percent, the number chosen by the AI will be re-picked by the same procedure and with a probability of $$$100-c$$$ percent, it will stay the same.

You have no idea how many times you already participated in this test and what numbers you have picked before, but you clearly want to spend as little time on it as possible. Therefore, you will choose a probability distribution $$$q_1, \dots, q_n$$$ and will say the number $$$k$$$ with the probability $$$q_k$$$.

What is the minimum expected number of guesses you need to make before completing the test?

Input

First line of input contains two integers $$$n$$$ and $$$c$$$ ($$$2 \leq n \leq 10^5$$$, $$$0 \leq c \leq 100$$$).

Second line of input contains $$$n$$$ integer numbers $$$p_1,\dots,p_n$$$ ($$$1 \leq p_i \leq 10^3$$$).

Output

Output a single floating-point number, which is the minimum possible expected number of guesses.

Your answer will be considered correct if its absolute or relative error doesn't exceed $$$10^{-6}$$$.

Examples
Input
4 100
25 25 25 25
Output
4
Input
2 0
1 4
Output
1.800000000
Note

For the purposes of this task, a probability distribution is a sequence of real numbers $$$q_1, \dots, q_n$$$ such that $$$0 \leq q_i$$$ and $$$q_1 + \dots + q_n=1$$$.