{ "type": "click", "from": 1754000000000, "to": 1756592000000,
  "count": 1234, "sum": 56789, "avg": 46.02,
  "p50": 123, "p95": 456, "p99": 789, "min": 1, "max": 50000 }

Semantics (all pinned; follow them exactly):

from/to are millisecond timestamps, inclusive, and optional (absent means unbounded). Non-numeric bounds, or from > to, are 400.
Only events of the given type within [from, to] are included.
sum is the exact integer sum of values.
avg is sum / count rounded half-up to two decimals.
Percentiles use the nearest-rank method: sort values ascending, take the value at 1-based rank ceil(p / 100 * count). No interpolation.
If no events match (including an unknown type), return 200 with count: 0, sum: 0 and avg, p50, p95, p99, min, max all null.
The response echoes the effective from/to (null when unbounded).

Performance requirement

The endpoint must stay fast at this data size: 2,000 mixed queries complete in under 6 seconds on this machine (the reference does it in ~1.5s). Precompute whatever you need at startup; per-query work must not scan the whole log.

Module contract

src/app.js is CommonJS and exports createApp() returning an http.Server that is not yet listening.
node src/index.js <port> starts the service.
No external dependencies. Run the tests with npm test.