{"raw_statement":[{"iden":"problem statement","content":"We have $N$ dice arranged in a line from left to right. The $i$\\-th die from the left shows $p_i$ numbers from $1$ to $p_i$ with equal probability when thrown.\nWe will choose $K$ adjacent dice, throw each of them independently, and compute the sum of the numbers shown. Find the maximum possible value of the expected value of this sum."},{"iden":"constraints","content":"*   $1 ≤ K ≤ N ≤ 200000$\n*   $1 ≤ p_i ≤ 1000$\n*   All values in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$\n$p_1$ ... $p_N$"},{"iden":"sample input 1","content":"5 3\n1 2 2 4 5"},{"iden":"sample output 1","content":"7.000000000000\n\nWhen we throw the third, fourth, and fifth dice from the left, the expected value of the sum of the numbers shown is $7$. This is the maximum value we can achieve."},{"iden":"sample input 2","content":"4 1\n6 6 6 6"},{"iden":"sample output 2","content":"3.500000000000\n\nRegardless of which die we choose, the expected value of the number shown is $3.5$."},{"iden":"sample input 3","content":"10 4\n17 13 13 12 15 20 10 13 17 11"},{"iden":"sample output 3","content":"32.000000000000"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}