Yesterday, when you were passing by the newsstand near your home, you saw an advertisement for lottery games. The advertisement said "Choose m different numbers between \textbf{1} and \textbf{n}, inclusive. We will also randomly pick \textbf{m} different numbers between \textbf{1} and \textbf{n}, inclusive, and if you have at least \textbf{k} numbers in common with us, you win!". You want to know the probability of winning this lottery game. \InputFile Each line is a separate test that contain three integers \textbf{n}, \textbf{m} and \textbf{k}. It is known that \textbf{2} ≤ \textbf{n} ≤ \textbf{8}, \textbf{1} ≤ \textbf{m} ≤ \textbf{n} - \textbf{1}, \textbf{1} ≤ \textbf{k} ≤ \textbf{m}. \OutputFile For each test case print in a separate line with \textbf{4} digits after the decimal point the probability of winning the lottery game.