Let $S_n$ be an integer sequence produced with the following pseudo-random number generator:

$$\begin{array}{rl}{S}_0& =290797\\ S_{n+1}& =S_n^{2}mod50515093\end{array}$$

Let $A(i,j)$ be the minimum of the numbers $S_i,S_{i+1},\dots ,S_j$ for $i\le j$.
Let $M(N)=\sum A(i,j)$ for $1\le i\le j\le N$.
We can verify that $M(10)=432256955$ and $M(10000)=3264567774119$.

Find $M(2000000000)$.