Let $f(n, x)$ be a function that denotes the number of ways to travel from $(0,0)$ to $(n, n)$ in a 2-dimensional grid without touching/crossing the diagonal formed by the points $(0, x)$ and $(n-x, n)$. From a given point $(a, b)$ you can either travel to $(a+1, b)$ or $(a, b+1)$ in one step.

Define $g(n) = \sum _{i=1}^{n} f(n, i)$

Calculate $g(100000)$ mod $10^{9}+7$

Example: $f(2, 1) = 2$, The two valid paths being -