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.
\n
Example 1:
\n\n\nInput: rolls = [3,2,4,3], mean = 4, n = 2\nOutput: [6,6]\nExplanation: The mean of all n + m rolls is (3 + 2 + 4 + 3 + 6 + 6) / 6 = 4.\n\n\n
Example 2:
\n\n\nInput: rolls = [1,5,6], mean = 3, n = 4\nOutput: [2,3,2,2]\nExplanation: The mean of all n + m rolls is (1 + 5 + 6 + 2 + 3 + 2 + 2) / 7 = 3.\n\n\n
Example 3:
\n\n\nInput: rolls = [1,2,3,4], mean = 6, n = 4\nOutput: []\nExplanation: It is impossible for the mean to be 6 no matter what the 4 missing rolls are.\n\n\n
\n
Constraints:
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