def __missing__(self, key):
        if self.default_factory is None:
            raise KeyError(key)
        else:
            ret = self[key] = self.default_factory(name=key)
            return ret
def kth(root, k):
    if k < size(root.left):
        return kth(root.left, k)
    elif k > size(root.left):
        return kth(root.right, k - size(root.left) - 1)
    return root.key