Do I need to setup the Integration Response and Method Response for each 400 error

When working with API Gateway Integration Response and Method Response. We have multiple 400 errors, they all return the same formated object but the status numer changes.

I think I am not understanding this correctly. Do I need to setup the Integration Response and Method Response for each 400 error. It is a lot of duplication, in the integration response I am only returning $input.path('$.errorMessage'); in the Mapping templates.

Is the Method response status code what is passed as the response code? Is there a way to create one 400 Integration Response and Method Response and dynamically change the status code that gets passed as the response?

List of 400 errors 401 Access denied 402 Account inactive 404 Not found 406 Not acceptable 408 Request timeout 422 Request not processed 429 Too many requests

Sample of lambda error response { status: 422, statusText: "Unknown Error", message: "Unable to process.":, errors: [error01,error02], }

Thank You