Maximal Score After Applying K Operations

Statement

You are given a 0-indexed array of integer nums and an integer k. Your task is to maximize a score through a series of operations. Initially, your score is set to $0$.

In each operation:

1. Select an index i (where $0 ≤$ i $<$nums.length).

2. Add the value of nums[i] to your score.

3. Replace nums[i] with ceil(nums[i] / 3).

Repeat this process exactly k times and return the highest score you can achieve.

The ceiling function ceil(value) is the least integer greater than or equal to value.

Constraints:

• $1 \leq$ nums.length, k $\leq 10^3$

• $1 \leq$ nums[i] $\leq 10^5$

Examples