In strange town Klahol rabbits behave in a strange way. Everything is strange, even holidays. And year somehow has \textbf{n} days. Complexity is also that nobody except rabbits know which day of the year is today. Days are numbers in simple way: integers from \textbf{1} to \textbf{n}. Derabbit Bryan came to the town. He was lucky find a calendar with all holidays in this wonderful town. Altogether there are \textbf{m} holidays. Bryan is interested in the mean for number of days till the closest coming holiday. \InputFile The first line contains two integers separated by space: \textbf{n} and \textbf{m} (\textbf{1} ≤ \textbf{n} ≤ \textbf{10^9}, \textbf{1} ≤ \textbf{m} ≤ \textbf{min(10}^6, \textbf{n)}). The second line contains \textbf{m} integers -- day numbers for holidays (integers from \textbf{1} to \textbf{n}). \OutputFile You need to output the mean for number of days till the closest holiday (derabbit can’t learn which day is today, he assumes each of days equally possible) as an irreducible fraction (see samples).