You have observations of n + m
6sided 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 i^{th}
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 <= 10^{5}
1 <= rolls[i], mean <= 6

