Suppose we choose two real numbers x, y \in[0,1] uniformly at random. Let p be the probability that the circle with center (x, y) and radius |x-y| lies entirely within the unit square [0,1] \times [0,1]. Then p can be written in the form \frac{m}{n}, where m and n are relatively prime nonnegative integers. Compute m^{2}+n^{2}.