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 1 and n, inclusive. We will also randomly pick m different numbers between 1 and n, inclusive, and if you have at least k numbers in common with us, you win!".
You want to know the probability of winning this lottery game.
Each line is a separate test that contain three integers n, m and k. It is known that 2 ≤ n ≤ 8, 1 ≤ m ≤ n - 1, 1 ≤ k ≤ m.
For each test case print in a separate line with 4 digits after the decimal point the probability of winning the lottery game.