Let C be the unit circle x^{2}+y^{2}=1. A point P is chosen randomly on the circumference of C, and another point Q is chosen randomly from the interior of C. Both these points are chosen independently and uniformly over their domains. Let R be the rectangle with sides parallel to the x and y-axes with diagonal P Q. Suppose the probability that no point of R lies outside of C is \frac{1000}{k \pi}. Find k.