Compute expected days until no whole pills

A bottle initially contains **H half-pills** and **W whole pills**. Each day: 1. You randomly select **one pill uniformly** from the bottle. 2. If it is a **half-pill**, you consume it entirely (it is removed). 3. If it is a **whole pill**, you consume **half** and put the **remaining half** back into the bottle. (So selecting a whole pill decreases the number of whole pills by 1 and increases the number of half-pills by 1.) You always consume exactly **half a pill per day**. Task: **Compute the expected number of days until the bottle contains no whole pills** (i.e., only half-pills remain). ### Input - Two integers `H` and `W`. ### Output - A floating-point number: the expected number of days until `W = 0`. ### Example instance - `H = 25`, `W = 25`. ### Constraints (for your implementation) - You may assume `0 ≤ H, W ≤ 200` (or similar), and you should output the expectation with reasonable precision (e.g., `1e-6`).