Find dfa's for the following languages on $=\{a,b\}.$

$($a$)L=\{w$:$|w|mod3=0\}$

$($b$){?}^{(w)}L=\{w$:$|w|mod50\}$

$($c$)L=\{w$:$n_a(w)mod3>1\}$

$($d$)L=\{w$:$n_a(w)mod3>n_b(w)mod3\}$