Suppose every term in the sequence $$1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, \cdots$$ is either $1$ or $2$. If there are exactly $(2k-1)$ twos between the $k^{th}$ one and the $(k+1)^{th}$ one, find the sum of its first $2014$ terms.