You are given an integer array timeReq and an integer splitTime. There are timeReq.length bacterial strains that need to be eliminated, where the bacterial strain at index i requires timeReq[i] units of time to be eliminated by a single white blood cell (WBC).

Initially, at time $0$, there is $1$ WBC. At any moment, an available WBC can perform one of the following actions:

• Split into $2$ new WBCs, which takes splitTime units of time.

• Eliminate an uneliminated bacterial strain i, which takes timeReq[i] units of time. Once a WBC begins eliminating a strain, it cannot be reused.

Return the minimum time required to eliminate all bacterial strains.

Constraints:

• $2 \leq$ timeReq.length $\leq 10^5$

• $1 \leq$ timeReq[i] $\leq 10^9$

• $1 \leq$ splitTime $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.