You are given an integer array rolls of length m, representing the results of $m$ observations from rolling a $6$ sided die with face values from $1$ to $6$. There are also $n$ missing observations.

You are also given an integer mean, which represents the average of all $n + m$ rolls.

Return an array of length n containing the missing roll values such that the average of all $n + m$ rolls is equal to mean. If multiple valid configurations exist, return any of them. If no valid configuration exists, return an empty array.

Note: The mean of a collection of values is the sum of the values divided by the total count of values.

Constraints:

• m $==$ rolls.length

• $1 \leq$ n, m $\leq 10^5$

• $1 \leq$ rolls[i], mean $\leq 6$

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.