# 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.

```
class Solution {
public int[] missingRolls(int[] rolls, int mean, int n) {
int knownRollTotal = 0;
for (int roll : rolls) {
knownRollTotal += roll;
}
int meanRollTotal = mean * (n + rolls.length);
int nRollTotal = meanRollTotal - knownRollTotal;
if (nRollTotal < n || nRollTotal > 6 * n) {
return new int[] {};
}
int val = nRollTotal / n;
int extra = nRollTotal % n;
int[] res = new int[n];
for (int i = 0; i < res.length; i++) {
res[i] = val + (i < extra ? 1 : 0);
}
return res;
}
}
```

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