LeetCode 641: Design Circular Deque
Using the same type for the deque contents and the sizes/indices (k, count, head, tail) feels wrong. At least, k and count should be std::vector::size_type.

Since you are backing up the deque with std::vector, making head and tail the std::vector::iterator looks more idiomatic.

k is not the most descriptive name. Consider capacity.

I am not sure that std::vector is the best container to back up the fixed size deque. After all, the point of std::vector is to have a dynamic size. std::array, or even a plain old C-style array, looks more natural.