A calculus problem by Shivam Jadhav

If $a_{1},a_{2},a_{3},........,a_{n}$ is a sequence of positive numbers which are in A.P with common difference 'd' and $a_{1}+a_{4}+a_{7}+.......+a_{16}=147$ , then $a_{1}+a_{16}=M$ $a_{1}+a_{6}+a_{11}+a_{16}=N$ Maximum value of $a_{1}a_{2}......a_{16}=(\frac{S}{W})^{16}$ here S and W are co-prime non-negative integers. Find $S+W+M+N$