Minimum Cost to Set Cooking Time

Given start digit, moveCost, pushCost and targetSeconds, find the minimum fatigue to enter up to four digits (zero-padded to MMSS) whose minutes*60 + seconds = targetSeconds, where each digit press costs pushCost and moving the finger between different digits costs moveCost (starting at startAt). The problem reduces to checking all valid minute/second splits that sum to targetSeconds and computing the minimal move+push cost for their digit sequences.