2028 - Find Missing Observations\.

Medium

You have observations of n + m 6-sided dice rolls with each face numbered from 1 to 6. n of the observations went missing, and you only have the observations of m rolls. Fortunately, you have also calculated the average value of the n + m rolls.

You are given an integer array rolls of length m where rolls[i] is the value of the <code>i^th</code> observation. You are also given the two integers mean and n.

Return an array of length n containing the missing observations such that the average value of the n + m rolls is exactly mean. If there are multiple valid answers, return any of them. If no such array exists, return an empty array.

The average value of a set of k numbers is the sum of the numbers divided by k.

Note that mean is an integer, so the sum of the n + m rolls should be divisible by n + m.

Example 1:

Input: rolls = 3,2,4,3, mean = 4, n = 2

Output: 6,6

Explanation: The mean of all n + m rolls is (3 + 2 + 4 + 3 + 6 + 6) / 6 = 4.

Example 2:

Input: rolls = 1,5,6, mean = 3, n = 4

Output: 2,3,2,2

Explanation: The mean of all n + m rolls is (1 + 5 + 6 + 2 + 3 + 2 + 2) / 7 = 3.

Example 3:

Input: rolls = 1,2,3,4, mean = 6, n = 4

Output: []

Explanation: It is impossible for the mean to be 6 no matter what the 4 missing rolls are.

Constraints:

• m == rolls.length

• <code>1 <= n, m <= 10⁵</code>

• 1 <= rolls[i], mean <= 6