You are given two positive integers, n and target.

An array nums is considered beautiful if it satisfies the following conditions:

• nums.length is equal to n.

• nums consists of pairwise distinct positive integers.

• There do not exist two distinct indices i and j such that nums[i] + nums[j] is equal to target.

Return the minimum possible sum of elements in a beautiful array.

Constraints:

• $1 \leq$ n $\leq 10^9$

• $1 \leq$ target $\leq 10^9$

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.