There is a finite state automaton over an alphabet sigma_3 = {0, 1, 2} that given a word omega = omega_1 omega_2... omega_k simga_3* accepts it it and only if sigma_i=1^k omega_i 0 mod 3. That is, the sum of symbols in omega is 0 modulo 3. This automaton is given in the figure below. Let simga_r = {0, 1, ..., r}, and let L_r, t = {omega = omega_1...omega_k simga_i=1^k omega_i = 0 mod t} for some r greaterthanorequalto 2 and t greaterthanorequalto 3. Construct a finite state automaton M_r, t = (Q, sigma_r, delta, q_0, F) that recognizes (accepts) the language L_r, t for some fixed r and t