Sreenath is on the surface of a sphere of radius $1$. He wants to hand-deliver a (belated) birthday cake to Bitcable as quickly as possible, which is located at a random point on the sphere. Unfortunately, Sreenath is also very hungry. After each second of travelling, Sreenath eats half of the remaining cake. Every time Sreenath consumes cake, his walking speed increases by $\frac{\pi}{32}$ units per second. Sreenath starts out with a walking speed of $\frac{\pi}{32}$ units per second. Let $p$ be the fraction of cake Bitcable can expect to receive. Compute the integer closest to $10000\cdot p$.