Minimize time using elevator then climb stairs

Problem

You need to go up n floors (from floor 0 to floor n). You may:

1. Take the elevator first (at most once, only at the start) for k floors, where 0 ≤ k ≤ n .
   • For each elevator floor traveled:
     • You gain e1 energy.
     • You spend t1 time.
   • After riding k floors, your energy is E = k * e1 .
2. Then climb the remaining n - k floors by stairs .
   • For each stair floor climbed:
     • If your current energy before climbing that floor is E , the time spent on that floor is:

$\lceil c / E \rceil$

 - After climbing that floor, your energy decreases by `e2`:
   
   `E := E - e2`

• Energy must never become negative , meaning before every stair step you must have E ≥ e2 (so that after subtracting e2 you still have E ≥ 0 ).

Your task is to choose k to minimize the total travel time.

Input

Five integers:

• n : number of floors to go up
• e1 : energy gained per elevator floor
• t1 : time per elevator floor
• e2 : energy spent per stair floor
• c : constant used in stair time formula

Output

Return the minimum possible total time to reach floor n.

• If it is impossible to reach floor n for any k (i.e., you can’t complete the stair portion without energy going negative), return -1 .

Notes / Clarifications

• The elevator can be taken only once and only before any stair climbing .
• Stair time uses the current energy before spending e2 for that floor.
• Use 64-bit arithmetic where appropriate.