random walk probability

There is dog walking(1 step at a time) on a path(1D) of size 'N' (N sites), one side of the path has a wall and on the other side there is a cliff. When it goes to the wall it will be come back into the path and when it reaches the farther end it will fell into the cliff. So now, I know there are N^2-X^2 number of steps the dog will walk on the path before it goes to cliff.('X' is the starting point). In those steps how many times it will visit each site on the path?
Please some one help me ASAP, I am not able to find it. Thanks