Build a single-page nap planner that helps users figure out the ideal nap length based on what time they want to wake up.

The user enters the current time (or it auto-fills with the system clock) and picks a desired wake-up time. The app calculates the total available nap window, then recommends one of three nap types:

- **Power Nap** (10–20 min) — quick refresh, no grogginess
- **Sleep Cycle Nap** (90 min) — full sleep cycle, wake up feeling rested
- **Full Nap** (use the whole remaining window)

For each recommendation, display a clear "Set alarm for..." target time and a short one-line description of how that nap type will feel when the user wakes up. If the available window is too short for even a power nap (under 10 minutes), show a friendly warning instead.

The UI should feel calm and sleepy — soft colors, large readable text, and a single prominent action. No saving, no accounts, no backend — just a pure time-math widget on one page.