(defunc how-many (x l)
  :input-contract (listp l)
  :output-contract (natp (how-many x l))
  (cond
   ((endp l) 0)
   (t
    (if (equal x (first l))
     (+ 1 (how-many x (rest l)))
     (how-many x (rest l))))))

(check= (how-many 1 '(1 2 3 4)) 1)
(check= (how-many 5 '(1 2 3 4)) 0)
(check= (how-many 'a '(a b a b b b)) 2)
(check= (how-many 'a '(b a b b a)) 2)

(defunc find-index (l x n hm)
  :input-contract (and (listp l) (natp n) (natp hm))
  :output-contract (or (natp (find-index l x n hm)) (equal nil (find-index l x n hm)))
  (cond
   ((endp l) nil)
   ((and (equal (first l) x) (equal hm 0)) n)
   ((equal (first l) x) (find-index (rest l) x (+ n 1) (- hm 1)))
   (t (find-index (rest l) x (+ n 1) hm))))


(check= (find-index '(a b c d) 'a 0 0) 0)
(check= (find-index '(a b c d) 'd 0 0) 3)
(check= (find-index '(a b c d a) 'a 0 1) 4)
(check= (find-index '(a b a c c d a) 'a 0 2) 6)
(check= (find-index '(a b a c c d a) 'a 0 3) nil)
(check= (find-index '(a b a c c d a) 'e 0 0) nil)

(defunc find-arrangement/acc (x y acc)
  :input-contract (and (listp x) (listp y) (listp acc))
  :output-contract (or (listp (find-arrangement/acc x y acc)) (equal nil (find-arrangement/acc x y acc)))
  (cond
   ((endp y) ())
   ((equal nil (find-index x (first y) 1 (how-many (first y) acc))) nil)
   (t (cons (find-index x (first y) 1 (how-many (first y) acc)) (find-arrangement/acc x (rest y) (cons (first y) acc))))))

(defunc find-arrangement (x y)
  :input-contract (and (listp x) (listp y))
  :output-contract (or (listp (find-arrangement x y)) (equal nil (find-arrangement x y)))
  (if (equal (len (find-arrangement/acc x y ())) (len y))
    (find-arrangement/acc x y ())
    nil))



(check= (find-arrangement '(a b c e f g) '(a b c e f g g)) nil)
(check= (find-arrangement '(a b c) '(a c b)) '(1 3 2))
(check= (find-arrangement '(a a) '(a a)) '(1 2))