Advanced AI Prompt for Terragrunt Remote State Inheritance Optimization

Act as a Terragrunt Architecture Expert. Design a strictly DRY (Don't Repeat Yourself) remote state configuration architecture. Create the master `terragrunt.hcl` file located at the [PARENT_CONFIG_PATH] root that programmatically generates and injects the S3 bucket and DynamoDB locking configurations into all nested [CHILD_MODULES] at runtime. Utilize the [BACKEND_BUCKET_PREFIX] string to standardize bucket naming. Provide the exact code utilizing the `path_relative_to_include()` built-in function to dynamically map the state file `key` to the specific folder structure of the child module. Write a technical brief explaining how this abstraction mathematically eliminates hundreds of lines of boilerplate code when managing an organization with over 100 disparate microservice workspaces.