Problem:
Score : 300 points

Problem Statement

You are given a string s.
Among the different substrings of s, print the K-th lexicographically smallest one.

A substring of s is a string obtained by taking out a non-empty contiguous part in s.
For example, if s = ababc, a, bab and ababc are substrings of s, while ac, z and an empty string are not.
Also, we say that substrings are different when they are different as strings.

Let X = x_{1}x_{2}...x_{n} and Y = y_{1}y_{2}...y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \neq y_{j}.

Constraints

1 ≤ |s| ≤ 5000

s consists of lowercase English letters.

1 ≤ K ≤ 5

s has at least K different substrings.

Partial Score

200 points will be awarded as a partial score for passing the test set satisfying |s| ≤ 50.

Input

Input is given from Standard Input in the following format:

s
K

Output

Print the K-th lexicographically smallest substring of K.

Sample Input 1

aba
4

Sample Output 1

b

s has five substrings: a, b, ab, ba and aba.
Among them, we should print the fourth smallest one, b.
Note that we do not count a twice.

Sample Input 2

atcoderandatcodeer
5

Sample Output 2

andat

Sample Input 3

z
1

Sample Output 3

z

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)


(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 1))
    #-swank '(optimize (speed 3) (safety 0) (debug 0))))

(defmacro print-line (obj &optional (stream '*standard-output*))
  `(prog1 (princ ,obj ,stream) (terpri ,stream)))


;; Hauptteil

(declaim (inline dict<))
(defun dict< (str1 str2)
  (declare #.OPT
           (base-string str1 str2))
  (let* ((len1 (length str1))
         (len2 (length str2))
         (len (min len1 len2)))
    (loop for i below len
          for c1 = (aref str1 i)
          for c2 = (aref str2 i)
          do (cond ((char< c1 c2) (return t))
                   ((char> c1 c2) (return nil)))
          finally (return (if (< len1 len2) t nil)))))

(declaim (inline enum-words))
(defun enum-words (source)
  (declare #.OPT
           (base-string source))
  (let ((len (length source))
        res)
    (dotimes (idx1 len res)
      (loop for width from 1 to 5
            while (<= (+ idx1 width) len)
            do (push (make-array width
                                 :element-type 'base-char
                                 :displaced-to source
                                 :displaced-index-offset idx1)
                     res)))))


(deftype uint nil `(integer 0 ,(expt 10 9)))
(defun main ()
  (declare #.OPT)
  (let ((str (coerce (read-line) 'base-string))
        (idx (- (read) 1)))
    (write-line (nth idx (sort (remove-duplicates (enum-words str)
                                                  :test #'string=)
                               #'dict<)))))

#-swank(main)