Jinx or Jackpot

Jack is in his favourite casino and has 1000 dollars. The casino has literally nothing but a single slot machine. Jack knows the history of this casino. Once upon a time, the future owner of the casino was walking and suddenly saw an array of n integer choices p_{1}, \dots, p_{n} each from 0 to 100. He picked an index i (1 \leq i \leq n) uniformly at random and thought that it was a good idea to create a casino in which there is only one slot machine with jackpot probability of \frac{p_i}{100}. And he created it.

Jack knows the array of choices p_{1}, \dots, p_{n} that suddenly appeared to the owner during the walk, but he does not know which i the owner picked. However, the chosen index i is fixed forever; the slot machine always uses the same p_i as explained below.

On the slot machine, Jack can bet x dollars, where x is a non-negative integer, and pull the lever. Then:

• With probability \frac{p_i}{100} it will be a jackpot, and the slot machine returns 2x dollars to him, so he gains x dollars.

• With probability 1 - \frac{p_i}{100} it will be a jinx, and the slot machine returns nothing to him, so he loses x dollars.

Even if Jack bets 0 dollars, he will understand whether it was a jinx or a jackpot.

Also, the slot machine is not very durable, so Jack can play at most k rounds on it.

Find the maximum expected profit Jack can achieve by an optimal strategy. Here a profit is defined as the final amount of money Jack has minus his initial 1000 dollars.

Of course, Jack can't make a bet that is more than his current balance.

Input

The first line contains two integers n and k (1 \leq n \leq 100\,000; 1 \leq k \leq 30) — the number of choices and the limit on the number of rounds. The second line contains n integers p_{1}, \dots, p_{n} (0 \le p_i \le 100) — the choices.

Output

Output a single real number — the expected profit Jack can achieve by an optimal strategy. Your answer will be considered correct if its absolute or relative error is at most 10^{-4}.

Examples

Input

2 2
70 30

Output

160

Input

2 30
30 70

Output

12099716.1778528057038784

Input

2 5
40 50

Output

0

Input

6 6
10 20 60 30 40 50

Output

29.40799999999990177457221

Input

1 5
61

Output

1702.708163199999489734182