Refund Workflow Engine on a DAG

Problem: Refund Workflow Engine on a DAG When a DoorDash order times out, a refund workflow needs to run several steps, such as: Validate refund eligibility. Calculate refund amount. Call the payment system to issue a refund. Notify the user. Write audit logs. These steps have dependencies and form a directed acyclic graph. Implement a workflow engine that executes all steps according to dependencies. For judging purposes, executing a step is simplified to outputting the nodes that can run in each parallel round. You are given n steps and m dependency edges. Edge A B means step B can run only after step A completes. Requirements: Return the execution plan grouped by rounds. Steps in the same round can run in parallel and should be printed in lexicographical order. If the graph has a cycle, print INVALID. Each step should execute only once; repeated API calls should be avoided through workflow-step idempotency keys. Input Format n m step_1 ... step_n from_1 to_1 ... from_m to_m Output Format If the graph is acyclic, print one line per parallel execution round, with step names separated by spaces. If there is a cycle, print: INVALID Constraints 1 <= n <= 2 * 10^5 0 <= m <= 2 * 10^5 Step names are strings without spaces. Example Input 5 4 validate calculate refund notify audit validate calculate calculate refund refund notify refund audit Output validate calculate refund audit notify