A population of N items contains K positives. Draw n without replacement. Return the probability of getting exactly k positives.

$$P = \frac{\binom{K}{k}\binom{N-K}{n-k}}{\binom{N}{n}}$$

Use this rather than the binomial whenever the population is small enough that removing an item noticeably changes the odds for the next one.

Input

N = 50
K = 5
n = 10
k = 1

Output

0.43133719722856767