Let $p(t)$ denote the $(t+1)$th prime number. So that $p(0)=2$, $p(1)=3$, etc.
We define the prime score of a list of nonnegative integers $[a_1,\dots ,a_n]$ as the sum $\sum _{i=1}^{n}p(a_i)$.
Let $M(k,n)$ be the maximal prime score among all lists $[a_1,\dots ,a_n]$ such that:

• $0\le a_i<k$ for each $i$;
• the sum $\sum _{i=1}^n{a}_i$ is a multiple of $k$.

For example, $M(2,5)=14$ as $[0,1,1,1,1]$ attains a maximal prime score of $14$.

Find $M(7000,p(7000))$.