from typing import List
import itertools


def find_first_invalid_xmas_num(xmas_nums: List[int], prev: int) -> int:
    """validate the numbers: each number (starting at index `prev`) must be
    the sum of to of the `prev` numbers. Return the first number that does not
    match this condition.
    Raise ValueError if all numbers are valid.
    """
    for i in range(prev, len(xmas_nums)):
        subset = xmas_nums[(i-prev):i]
        if xmas_nums[i] not in [sum(x) for x in itertools.combinations(subset, 2)]:
            return xmas_nums[i]

    raise ValueError("no invalid nums found")