You have observations of
n + m 6-sided dice rolls with each face numbered from
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
rolls[i] is the value of the
ith observation. You are also given the two integers
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
mean is an integer, so the sum of the
n + m rolls should be divisible by
n + m.
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.
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.
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.
m == rolls.length
1 <= n, m <= 105
1 <= rolls[i], mean <= 6