There is a circle of red and blue tiles represented by an integer array colors and an integer k. The color of tile i is denoted by colors[i], where colors[i] is equal to $0$ for a red tile and $1$ for a blue tile.

An alternating group is defined as a sequence of k contiguous tiles in the circle such that every adjacent pair of tiles in the sequence has alternating colors, meaning every tile has a different color from its adjacent neighbors within the sequence.

Return the total number of alternating groups of length k.

Note: Because colors represents a circle, the first tile and the last tile are adjacent.

Constraints:

• $3 \leq$ colors.length $\leq 10^5$

• $0 \leq$ colors[i] $\leq 1$

• $3 \leq$ k $\leq$ colors.length

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