Dijkstras algorithm was applied to a given directed and connected graph G = (V,E) with positive edge weights starting from the node s. The shortest path from s to another node in the graph t was recorded. Then, the graph was modified by doubling the weight of each edge. Lets call the modified graph G. Dijkstras algorithm was then executed on G and the shortest path from s to t was also recorded. Would the shortest path from s to t in G be the same as that of G (i.e., both will have the same set of nodes). If yes, provide a proof; otherwise, provide a counter example.