n people each have a birthday drawn uniformly from d equally likely days. Return the probability that at least two of them share one.

Go through the complement and place people one at a time: the second person must avoid 1 day, the third must avoid 2, and so on.

$$P(\text{collision}) = 1 - \prod_{i=0}^{n-1}\frac{d-i}{d}$$

Input

n = 23
d = 365

Output

0.5072972343239857