AMC 12A 2025 (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

\text{(A)}\;8

\text{(B)}\;9

\text{(C)}\;10

\text{(D)}\;11

\text{(E)}\;12