Construct an pda for the language generated by this grammar:

S$->$ aSB$|$ bA

A $->$ aA$|$ a

B $->$ bBB$|$b

$($a$)$ Show the general state diagram of such pda constructed from grammar rules.

$($b$)$ Add edge transitions $($input symbol, top stack symbol, output string$)$ from production rules to the above diagram.