Please answer fast to this AI problem.

The agent is planning a fastest path from $S$ to $Z$ on the following static board. The move can be taken from every grid to its adjacent grid either up$,$ down, left, or right. The grid coloured 'with grey cannot be reached by the agent. Answer the following questions.

$\backslash$table$[[$U$,,]]$

A$.$ Draw the full search tree for BFS $($breadth$-$frist search$)$ exploring the board. Note that the search may return to the nodes that have been visited already; and you must include all leaf nodes at the depth that the goal state $Z$ is reached. For example, if the goal state is reached at depth $3$ from a certain branch, the leaf nodes for all other branches at depth $3$ or less must be shown.

B$.$ Based on the description in $($A$),$ we are now using DFS $($depth$-$first search$)$ provided with the following instructions.

Move up whenever possible

Move right whenever possible if up is not possible

Move down whenever possible if up and right are not possible

Move left, otherwise

Will DFS succeed? If yes, show the path. If no$,$ why not?