AMC 12 2025a Problem 21

There is a unique ordered triple $(a,k,m)$ of nonnegative integers such that $$\frac{4^a + 4^{a+k}+4^{a+2k}+\cdots + 4^{a+mk}}{2^a + 2^{a+k} + 2^{a+2k}+ \cdots + 2^{a+mk}} = 964.$$ What is $a+k+m$?

$\textbf{(A) } 8 \textbf{(B) } 9 \textbf{(C)} 10 \textbf{(D) } 11 \textbf{(E) } 12$