Eccoci.

The sequence $S_n$ is defined by $S_0 = 290797$ and $S_n = S_{n - 1}^2 \bmod 50515093$ for $n > 0$.

There are $N$ bowls indexed $0,1,\dots ,N-1$. Initially there are $S_n$ beans in bowl $n$.

At each step, the smallest index $n$ is found such that bowl $n$ has strictly more beans than bowl $n+1$. Then one bean is moved from bowl $n$ to bowl $n+1$.

Let $B(N)$ be the number of steps needed to sort the bowls into non-descending order.
For example, $B(5) = 0$, $B(6) = 14263289$ and $B(100)=3284417556$.

Find $B(10^7)$.