# 2028 Find Missing Observations

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 `ith` 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`
• `1 <= n, m <= 105`
• `1 <= rolls[i], mean <= 6`
 ``````1 2 3 4 5 6 7 8 9 `````` ``````class Solution: def missingRolls(self, rolls: List[int], mean: int, n: int) -> List[int]: x = mean * (len(rolls) + n) - sum(rolls) if x < n or x > n * 6: return [] res = [x // n] * n for i in range(x % n): res[i] += 1 return res``````