$(20$ points$)$ For the given weighted graph G$,$ execute Prim's algorithm to find a minimum spanning tree, starting from vertex A$.$ Show the MST $($by darkening the edges of the graph that are part of the MST$)$ and fill the table below that gives the final values of key and pointer for each vertex.

$\backslash$table$[[$Vertex$,$A$,$B$,$C$,$D$,$E$,$F$,$G$],[$Key$($v$),0,,,,,,],[P(v),$null,,,,,,$]]$