Harvey is set on a mission to test his luck. To test a person’s luck there is a circular room which is marked with $180$ points with numbers $1,2,3, \cdots, 180$ written on them on the circumference equidistant from the adjacent points. Harvey stands at the point $1$ on the boundary with a gun in his hand. He shoots the gun aiming inside the circle at any of the marked points from $2$ to $90$ ($90$ included). Assuming an elastic collision between the bullet and the wall the bullet reflects as soon as it touches any point on the circumference. If the bullet reaches the point $1$ it hits Harvey and he dies.The bullet stops when it reaches a point where the number written on it is smaller than that of the number written on the point from which it was reflected.

Given that Harvey chooses the point where he shoots randomly, let the probability that Harvey dies in the game be $\frac{m}{n}$ ($m$ and $n$ are coprime). Enter your answer as $m \cdot n$.