Everyone knows OR operation. Let us define new operation which we will call Probablistic OR. We will denote this operation as \textbf{#}. For given real number \textbf{p} (\textbf{0} ≤ \textbf{p} ≤ \textbf{1}) and two bits a and b: \begin{itemize} \item if \textbf{a} = \textbf{1} and \textbf{b} = \textbf{1}, then \textbf{#}(\textbf{a}, \textbf{b}) = \textbf{1}; \item if \textbf{a} = \textbf{0} and \textbf{b} = \textbf{0}, then \textbf{#}(\textbf{a}, \textbf{b}) = \textbf{0}; \item else \textbf{#}(\textbf{a}, \textbf{b}) = \textbf{0} with probability \textbf{p}, \textbf{#}(\textbf{a}, \textbf{b}) = \textbf{1} with probability \textbf{1-p}. \end{itemize} Now for two given non-negative integers \textbf{x} and \textbf{y} we can define bitwise Probablistic OR operation. The result of this operation is a number received by performing \textbf{#} operation for each pair of bits of \textbf{x} and \textbf{y} in same positions. For example, for \textbf{p} = \textbf{0.5}, \textbf{x} = \textbf{2}, and \textbf{y} = \textbf{4}, we will get \textbf{0}, \textbf{2}, \textbf{4} or \textbf{6} each with probability \textbf{0.25}. You will be given a list of non-negative integers. You have to implement a program which will calculate the expected value of the result of performing bitwise probablistic OR operation on all these numbers given some \textbf{p}. The numbers will be taken from left to right. \InputFile Input file starts with real number \textbf{p} (\textbf{0} ≤ \textbf{p} ≤ \textbf{1}) with exactly two digits after the decimal point. Integer \textbf{n} follows (\textbf{1} ≤ \textbf{n} ≤ \textbf{100}). Next line contains \textbf{n} numbers ai in the order they are taking part in the operation (\textbf{0} ≤ \textbf{a_i} ≤ \textbf{10^9}). \OutputFile Output the expected value of performing Probablistic OR operation on the given numbers for given \textbf{p}. Print the result with two digits after the decimal point.