You are given an integer array nums and an integer k. Append k unique positive integers that do not appear in nums such that the sum of the appended integers is minimized.

Return the sum of the k integers appended to nums.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

• $1 \leq$ k $\leq 10^8$

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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.