def ladder(a: list[int], b: list[int]) -> list[int]:
    size = len(a)
    mod = (1 << max(b)) - 1

    fib = [0, 1]
    for i in range(2, max(a) + 2):
        fib.append((fib[i - 1] + fib[i - 2]) & mod)

    result = [0] * size
    for i in range(size):
        result[i] = fib[a[i] + 1] & ((1 << b[i]) - 1)

    return result