A random forest picks m distinct features at random out of d, of which r are genuinely informative. Return the probability the split sees at least one informative feature.

Complement again: count the ways to choose m features entirely from the d - r useless ones.

$$P(\text{at least one}) = 1 - \frac{\binom{d-r}{m}}{\binom{d}{m}}$$

Input

d = 100
r = 10
m = 10

Output

0.6695237889132748