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. 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 a single real number —