[1;10;1101] [0;1011;1]
(* shortest solution of length 119 *)
(* 1 0 1 1 0 2 1 0 1 0 1 1 0 1 1 0 2 1 1 0 2 1 0 1 0 2 1 2 1 1 0 1 2 0 2 2 1 1 0 2 0 1 0 2 1 1 1 0 1 0 1 0 2 2 1 1 0 1 1 0 1 0 2 2 1 1 0 2 1 1 0 1 0 2 2 1 0 1 0 2 1 1 0 1 0 2 1 1 2 1 0 2 1 1 2 1 0 2 0 2 1 2 2 0 2 1 1 2 0 2 1 0 2 2 1 2 2 0 2 *)