This problem is about finding a route on a square grid.The starting point is $(1,1)$ and the target point $(n,m)$.I can move each step from my current point $(x,y)$ either to $(x+y,y)$ or $(x,y+x)$.Now I need to determine if there is a path from $(1,1)$ to $(n,m)$, and if so to return the shortest one.Now I believe that if I trace back my steps from the input point $(n,m)$ I can always know which move I made out of the two possible ones since if $n=m$ then there is no route, this means I'm always take the smaller coordinate and subtract it from the bigger one.But that means I have at most only one possible route to $(n,m)$ so why was  I asked to return the shortest one?Am I missing anything ?
Route on a square grid with only (x,y)  (x,x+y) and (x,y)  (x+y,y) moves
algorithms;graph theory;shortest path;square grid