Shuffle a objects of type A together with b of type B into a random order. Return the expected number of adjacent pairs whose two items share a type.

Linearity of expectation does all the work: there are $a + b - 1$ adjacent positions, and each one holds a matching pair with the same probability.

$$P(\text{match}) = \frac{a(a-1) + b(b-1)}{(a+b)(a+b-1)}$$

Input

a = 5
b = 5

Output

4.0