With a $\mathrm{Beta}(\alpha, \beta)$ prior and observed heads and tails, return the MAP estimate of the success probability.

$$\hat{p}_{\text{MAP}} = \frac{\text{heads} + \alpha - 1}{\text{heads} + \text{tails} + \alpha + \beta - 2}$$

The prior acts as pseudo-counts. With $\alpha = \beta = 1$ it is flat and the MAP collapses to the MLE, which is why that choice is the "no opinion" prior.

Input

alpha = 2.0
beta = 2.0
heads = 7
tails = 3

Output

0.6666666666666666