Combinations, Coordinate Geometry

[swerve]

A \(16\)-step path is to go from \((-4,-4)\) to \((4,4)\) with each step increasing either the \(x\)-coordinate or the \(y\)-coordinate by \(1.\) How many such paths stay outside or on the boundary of the square \(-2 \leq x \leq 2,\) \(-2 \leq y \leq 2\) at each step?

A. \(92\)
B. \(144\)
C. \(1,568\)
D. \(1,698\)
E. \(12,800\)

The OA is D