2024 Mock AMC 12 - Problem 5

Shiro has 26 unique blocks arranged in a circle and wants to add 5 stickers to the blocks, labelled 1, 2, 3, 4, 5. He starts by choosing any starting block to add the first sticker to. Each subsequent sticker must be separated from the previous one by no more than 4 blocks. A block may have multiple stickers but the same block cannot be chosen consecutively. How many distinct combinations of blocks and stickers are possible?

\textbf{(A) }16250\qquad\textbf{(B) }2600000\qquad\textbf{(C) }100000\qquad\textbf{(D) }11881376\qquad\textbf{(E) }260000