Create Maximum Number

Given two arrays of digits `nums1` and `nums2` (each element is a single digit 0-9), and an integer `k`, return an array of length `k` that contains the maximum number that can be formed by choosing digits from both arrays. The relative order of digits from the same original array must be preserved in the final number. You may choose any number of digits (including zero) from each array, but the total chosen must be exactly `k`. If it is impossible to choose exactly `k` digits, return an empty list. Implement the function `max_number(nums1, nums2, k)`. **Details:** - You can pick `i` digits from `nums1` and `k-i` digits from `nums2` for any valid `i` (0 ≤ i ≤ len(nums1), 0 ≤ k-i ≤ len(nums2)). - The resulting sequence must preserve the order of digits as they appear in each original array. - Among all possible valid selections, return the lexicographically largest (as a list of digits). - If no such `i` exists, return an empty list. Examples are provided below.

```python
# Example 1
nums1 = [3, 4, 6, 5]
nums2 = [9, 1, 2, 5, 8, 3]
k = 5
# The largest number is [9, 8, 6, 5, 3]
print(max_number(nums1, nums2, k))  # [9, 8, 6, 5, 3]

# Example 2
nums1 = [6, 7]
nums2 = [6, 0, 4]
k = 5
# The largest number is [6, 7, 6, 0, 4]
print(max_number(nums1, nums2, k))  # [6, 7, 6, 0, 4]

# Example 3
nums1 = [3, 9]
nums2 = [8, 9]
k = 3
# The largest number is [9, 8, 9]
print(max_number(nums1, nums2, k))  # [9, 8, 9]
```