Let $f(x,y)$ $=$ $\sqrt{x\sqrt{(x+1)\sqrt{(x+2)....\sqrt{(y-1)\sqrt{y}}}}}$ for $x>=2$ and $x$ $<$ $y$ where $x$ and $y$ are integers.

Also, let $g(x)$ $=$ $T$ where $T$ is the smallest integer such that $x$ $<$ $T$.

Let $h(x)$ $=$ $2^x$ $mod$ $1000000007$

Find out $h((g(f(g(f(42,111111111111111)),222222222222222)))))$.