def num_cycle_scenarios(k):
    """Compute the number (and the length) of scenarios for a cycle with
    the given size."""

    if k % 2 == 1:
        print("ERROR: Odd cycle size.")
        exit(-1)
    
    l = (k // 2) - 1
    s = (l + 1) ** (l - 1)
    return s, l