Some Fibonacci numbers are immune to zombie attack - as prime numbers they can't be decomposed. Fibonacci numbers are defined by the following recurrence: \includegraphics{https://static.e-olymp.com/content/54/54217ddf6fc583d7640d1f0982545c315014ce43.jpg} \includegraphics{https://static.e-olymp.com/content/71/71ed8be2ac94b3db320249481fde7c0e39117d5b.jpg} \includegraphics{https://static.e-olymp.com/content/64/64aaabc8585f507befd86e944c9f745318171ab2.jpg} You will be given an indefinite number of integer ranges of numbers that can be represented as \textbf{64}-bit signed integers. Your job is to report in increasing order the Fibonacci numbers that fall within that range, as well as their base-\textbf{2} logarithm and their prime decomposition - the prime numbers in increasing order which, when multiplied together, give the value of the Fibonacci number. If there is no Fibonacci number in the range, report that fact. \textit{\textbf{Reminder:}} \begin{itemize} \item the logarithm of zero is undefined, even though zero is the first Fibonacci number. Also note that, by definition, \textbf{0} and \textbf{1} have no prime factors, even though they are Fibonacci numbers. \item to calculate the base \textbf{c} logarithm, note that \textbf{ log_c(x) = log(x)/log(c)}, using on the right-hand side your favorite logarithm (common logarithm or natural logarithm). \end{itemize} \InputFile The input file contains an indeterminate number of lines consisting of two non-negative integers (\textbf{lo} and \textbf{hi}) separated by one space, given in hexadecimal format (as in \textbf{0x1a} meaning \textbf{26} in decimal). Each integer is guaranteed to fit within a \textbf{64}-bit signed integer. The program terminates when it either encounters an end-of-file condition or when \textbf{lo} > \textbf{hi}. \OutputFile For each range in the input file, print the range and the Fibonacci number information as shown in the sample output, with each range separated by a blank line. Note that the base-\textbf{2} logarithm (\textbf{lg}) is reported with six digits to the right of the decimal point, and that the prime factors are separated by single spaces.