def increment_pair(pair):
    """
    Increments pair by traversing through all
    k for a given j until 1 is reached, then starting
    back up with the next highest value for j

    E.G. [1,2]-->[2,3]-->[1,3]-->[3,4]-->[2,4]-->...
    """
    k, j = pair
    k -= 1
    if k > 0:
        return [k, j]
    else:
        return [j, j + 1]