```python
"""A block-allocation bitmap: 32-bit words, LSB-first, a set bit is occupied."""

WORD_BITS = 32
WORD_MAX = 0xFFFFFFFF


def _whole(value):
    return not isinstance(value, bool) and isinstance(value, int)


def _check_words(words):
    for word in words:
        if not _whole(word) or word < 0 or word > WORD_MAX:
            raise ValueError("bitmap words must be integers from 0 to 4294967295")


def _bit_of(words, index):
    return (words[index // WORD_BITS] >> (index % WORD_BITS)) & 1


def bit_at(words, index):
    _check_words(words)
    if not _whole(index):
        raise ValueError("bit index must be an integer")
    if index < 0 or index >= len(words) * WORD_BITS:
        raise ValueError("bit index is outside the words")
    return _bit_of(words, index)


def occupy_run(words, start, length):
    _check_words(words)
    if not _whole(start) or start < 0:
        raise ValueError("run start must be a non-negative integer")
    if not _whole(length) or length <= 0:
        raise ValueError("run length must be a positive integer")
    if start + length > len(words) * WORD_BITS:
        raise ValueError("run leaves the words")
    for i in range(start, start + length):
        if _bit_of(words, i) == 1:
            raise ValueError("run touches an occupied block")
    marked = list(words)
    for i in range(start, start + length):
        marked[i // WORD_BITS] |= 1 << (i % WORD_BITS)
    return marked


def find_free_run(words: list, capacity: int, length: int) -> int:
    if not _whole(capacity) or capacity <= 0:
        raise ValueError("capacity must be a positive integer")
    word_count = (capacity + WORD_BITS - 1) // WORD_BITS
    if len(words) != word_count:
        raise ValueError("word count disagrees with the capacity")

    if length <= 0:
        raise ValueError("run length must be a positive integer")

    # Check for stray bits at or beyond the capacity
    for i in range(capacity, len(words) * WORD_BITS):
        if _bit_of(words, i) != 0:
            raise ValueError(f"stray bit at index {i} beyond capacity {capacity}")

    start = -1
    word_index = 0

    while word_index < len(words):
        free_bits_in_word = WORD_BITS - bin(words[word_index]).count('1')
        if free_bits_in_word >= length:
            start = word_index * WORD_BITS + (WORD_BITS - free_bits_in_word)
            return start
        word_index += 1

    return -1
```