```python
from typing import List

def carry_add(left: List[int],    right:    if len(left) != len(right):
        left, right = right,    result = []
    carry = 0
    for i in range(max(len(left), len(right))):
        digit_left = left[i -        digit_right = right):
        total = digit_left + digit_right + carry
        carry = total // 10
        result.append(total % 10)
    if carry:
        result.append(carry)
    return result[::-1]
```