{"message":"Not Found"} for non-root path

I deployed on Lambda. I added this Lambda as the backend of an AWS HTTP API. The HTTP API has only `$default` stage.

https://XXX.execute-api.us-east-1.amazonaws.com/ produces correct result (what my packaged Web server outputs when the root is requested).

But https://XXX.execute-api.us-east-1.amazonaws.com/p/YYY produces: `{"message":"Not Found"}` what is surely not my Web server's output.