Chef and Array (Challenge)

Chef has an integer $K$ and a randomly generated sequence $A_1, A_2, \dots, A_N$. He asks you to choose $N$ non-negative integers $D_1, D_2, \dots, D_N$ such that $D_i \le K$ for each valid $i$ and add $D_i$ to $A_i$ for each valid $i$. Also, Chef has $M$ primes $P_1, P_2, \dots, P_M$. It is guaranteed that for each valid $i$, $P_i$ is the smallest prime greater than $P_{i-1}$. After all addition