Let $t_k$ be the tribonacci numbers defined as:
$t_0=t_1=0$;
$t_2=1$;
$t_k=t_{k-1}+t_{k-2}+t_{k-3}\text{ for }k\ge 3$.

For a given integer $n$, let $A_n$ be an array of length $n$ (indexed from $0$ to $n-1$), that is initially filled with zeros.
The array is changed iteratively by replacing $A_n[(t_{2i-2}modn)]$ with $A_n[(t_{2i-2}modn)]+2(t_{2i-1}modn)-n+1$ in each step $i$.
After each step $i$, define $M_n(i)$ to be ${\displaystyle max\{\sum _{j=p}^q{A}_n[j]:0\le p\le q<n\}}$, the maximal sum of any contiguous subarray of $A_n$.

The first 6 steps for $n=5$ are illustrated below:
Initial state: $A_5=\{0,0,0,0,0\}$
Step 1: $\Rightarrow A_5=\{-4,0,0,0,0\}$, $M_5(1)=0$
Step 2: $\Rightarrow A_5=\{-4,-2,0,0,0\}$, $M_5(2)=0$
Step 3: $\Rightarrow A_5=\{-4,-2,4,0,0\}$, $M_5(3)=4$
Step 4: $\Rightarrow A_5=\{-4,-2,6,0,0\}$, $M_5(4)=6$
Step 5: $\Rightarrow A_5=\{-4,-2,6,0,4\}$, $M_5(5)=10$
Step 6: $\Rightarrow A_5=\{-4,2,6,0,4\}$, $M_5(6)=12$

Let ${\displaystyle S(n,l)=\sum _{i=1}^l{M}_n(i)}$. Thus $S(5,6)=32$.
You are given $S(5,100)=2416$, $S(14,100)=3881$ and $S(107,1000)=1618572$.

Find $S(10000003,10200000)-S(10000003,10000000)$.