A clock sequence is a periodic sequence of positive integers that can be broken into contiguous segments such that the sum of the $n$-th segment is equal to $n$.

For example, the sequence $$1234321234321234321\cdots$$ is a clock sequence with period $6$, as it can be broken into $$1|2|3|4|32|123|43|2123|432|1234|32123|\cdots$$ Let $C(N)$ be the number of different clock sequences with period at most $N$. For example, $C(3)=3$, $C(4)=7$ and $C(10)=561$.

Find $C({10}^4)mod1111211113$.