(defun all-lists-repeat (m k)
  (search k m 'list-repeat-expand)
)

(defun all-lists-no-repeat (m k)
  (search k m 'list-no-repeat-expand)
)

(defun all-bags-repeat (m k)
  (remove-duplicates (search k m 'bags-repeat-expand) :test #'tree-equal)
)

(defun all-bags-no-repeat (m k)
  (remove-duplicates (search k m 'bags-no-repeat-expand) :test #'tree-equal)
)


(defun search (k m expand)
  (do
    (
      (items (make-list k))
      (queue (mapcar 'list (make-list k)) (append (cdr queue) expansion))
      (expansion)
    )
    ((EQUAL (length (car queue)) m) queue)
    (setq expansion (funcall expand (car queue) items))
  )
)

(defun list-repeat-expand (queue items)
  (mapcar #'(lambda (x) 
              (cons x queue)
            )
            items)
  )
)

(defun list-no-repeat-expand (queue items)
  (remove nil 
    (mapcar #'(lambda (x) 
                (cond
                  ((not (member x queue)) (cons x queue))
                )
              )
              items)
    )
  )
)

(defun bags-repeat-expand (queue items)
  (mapcar #'(lambda (x) 
              (mergesort (cons x queue))
            )
            items)
  )
)

(defun bags-no-repeat-expand (queue items)
  (remove nil 
    (mapcar #'(lambda (x) 
                (cond
                  ((not (member x queue)) (mergesort (cons x queue)))
                )
              )
              items)
    )
  )
)


(defun make-list (m)
  (DO
    (
      (L () (CONS (BUILD-NAME "a" N) L))
      (N M (- N 1))
    )
    ((ZEROP N) L)
  )
)

(defun build-name (&rest names)
  (read-from-string (build-string names))
)

(defun build-string (name-list)
  (cond
    ((null name-list) nil) 
    (t (concatenate 
         'string 
         (cond
           (
             (numberp (car name-list))
             (princ-to-string (car name-list))
           )
           (
             t
             (string (car name-list))
           )
         )
         (build-string (cdr name-list))
       )
    )
  )
)