Maximize points with limited coworker skips

You and a coworker must unload a sequence of warehouses. For warehouse i there are c[i] items (non‑negative integers). Turns alternate starting with you: on your turn you remove exactly m items; on the coworker’s turn they remove exactly n items (m,n are positive integers). If your move empties a warehouse (i.e., the last removal that makes its remaining items ≤ 0 is yours), you earn 1 point for that warehouse; otherwise you earn 0. You must alternate turns, except you may spend up to k total skip tokens across all warehouses: spending one token on the coworker’s upcoming turn causes them to skip that turn and you immediately take the next turn instead; skips may be used multiple times on the same warehouse or spread across warehouses, but the total number of skips used across all warehouses must be ≤ k. Determine the maximum total points you can earn, and design an algorithm to compute it efficiently. State the time and space complexity.