Passing HTTP Headers from API Gateway HTTP API to Step Function?

I'm using SAM and I want to connect an HTTP POST endpoint from API Gateway to an AWS Step Function. I'm able to forward the request body but I'm unable to also pass the headers. This is my YAML definition:

  /cancelOrder:
    post:
      responses:
        default:
          description: "zzzz"
      x-amazon-apigateway-integration:
        integrationSubtype: "StepFunctions-StartExecution"
        credentials:
          Fn::GetAtt: [zzzz, Arn]
        requestParameters:
          Input: "$request.body"
          StateMachineArn:
            Fn::GetAtt: [zzzz, Arn]
        payloadFormatVersion: "1.0"
        type: "aws_proxy"
        connectionType: "INTERNET"
        timeoutInMillis: 10000

This works but I'm only able to receive the HTTP POST body, not the headers. Input: "$request.body" is, I suppose, the part that's parsing the JSON and sending it to my function. But I need both the Body and the HTTP headers.

Is there a way to do this?