Consider the following grammar for simple assignment statements:

AssignStmt Var = E

Var id | id [ Index ]

Index E

E Var | nr | E + E | E E | E * E | E / E | (E)

(a) (12 pts) Build a parse tree for each of the following assignment statements: a[2] = b + 1 x = v[k-3]

(b) (7 pts) Rewrite the grammar so that it allows multi-dimensional arrays (instead of just one index, allow a list of indices separated by commas). For instance, each of the following should be a valid string under the new grammar: m[5,3] = x y = p[i+1,j,k-1]