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`