(define (permute n p)
  (letrec (
      (make-list (lambda (n)
        (if (zero? n)
          '()
          (cons n (make-list (- n 1))))))

      (lremove-iterator (lambda (index input-list reversed-output-list)
        (if (zero? index)
          (append (reverse reversed-output-list) (cdr input-list))
          (lremove-iterator
            (- index 1)
            (cdr input-list)
            (cons (car input-list) reversed-output-list)))))

      (lremove (lambda (list index)
        (lremove-iterator index list '())))

      (lindex (lambda (list index)
        (if (zero? index)
          (car list)
          (lindex (cdr list) (- index 1)))))

      (permute-iterator (lambda (n p input-list output-list)
        (if (zero? n)
          output-list
          (let
            ((index (remainder p n)))
            (permute-iterator
              (- n 1)
              (quotient p n)
              (lremove input-list index)
              (cons (lindex input-list index) output-list)))))))

    (permute-iterator n p (make-list n) '())))