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from itertools import zip_longest

def broadcast_shape(a, b):
    a, b = tuple(a), tuple(b)
    if any(type(d) is not int or d < 0 for d in a + b):
        raise ValueError("dimension.invalid")
    result = []
    for left, right in zip_longest(reversed(a), reversed(b), fillvalue=1):
        if left == right or right == 1:
            result.append(left)
        elif left == 1:
            result.append(right)
        else:
            raise ValueError("shape.incompatible")
    return tuple(reversed(result))