Given that

$\frac{P_n}{Q_n} = 0 + \frac{1}{1 + \frac{1}{2 + \frac{1}{.... \frac{1}{(n-1) + \frac{1}{n}}}}}$

for $n>0$ ($n$ is an integer) where

$P_{0}$ = 0 and

$Q_{0}$ = 1.

Calculate ($P_{1000} * Q_{1000}) mod (1000000007)$