Problem:
﻿Score: 300 points

Problem Statement

Mr. Infinity has a string S consisting of digits from 1 to 9. Each time the date changes, this string changes as follows:

Each occurrence of 2 in S is replaced with 22. Similarly, each 3 becomes 333, 4 becomes 4444, 5 becomes 55555, 6 becomes 666666, 7 becomes 7777777, 8 becomes 88888888 and 9 becomes 999999999. 1 remains as 1.

For example, if S is 1324, it becomes 1333224444 the next day, and it becomes 133333333322224444444444444444 the day after next.
You are interested in what the string looks like after 5 \times 10^{15} days. What is the K-th character from the left in the string after 5 \times 10^{15} days?

Constraints

S is a string of length between 1 and 100 (inclusive).

K is an integer between 1 and 10^{18} (inclusive).

The length of the string after 5 \times 10^{15} days is at least K.

Input

Input is given from Standard Input in the following format:

S
K

Output

Print the K-th character from the left in Mr. Infinity's string after 5 \times 10^{15} days.

Sample Input 1

1214
4

Sample Output 1

2

The string S changes as follows:

Now: 1214

After one day: 12214444

After two days: 1222214444444444444444

After three days: 12222222214444444444444444444444444444444444444444444444444444444444444444

The first five characters in the string after 5 \times 10^{15} days is 12222. As K=4, we should print the fourth character, 2.

Sample Input 2

3
157

Sample Output 2

3

The initial string is 3. The string after 5 \times 10^{15} days consists only of 3.

Sample Input 3

299792458
9460730472580800

Sample Output 3

2

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (progn (ql:quickload '(:cl-debug-print))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)

(deftype int32 () '(signed-byte 32))
(deftype int64 () '(signed-byte 64))


;;macros
(defmacro println (n)
  `(format t "~a~%" ,n))
(defmacro vint-out (vec)
  `(progn
     (rep i (length ,vec)
          (princ (vref ,vec i))
          (princ " "))
     (fresh-line)))


;;vector
(defmacro vec (type &optional (num 100) (val 0))
  (let* ((g (gensym)))
    `(let* ((,g ,num))
       (make-array ,g :element-type ',type :initial-element ,val
                   :adjustable nil :fill-pointer ,g))))

(defmacro double-vec (type &optional (dim1 100) (dim2 100) (val 0))
  `(make-array '(,dim1 ,dim2) :element-type ',type :initial-element ,val))

(defmacro vint (&optional (num 0) (val 0))
  `(vec int32 ,num ,val))

(defmacro double-vec (type &optional (dim1 100) (dim2 100) (val 0))
  `(make-array '(,dim1 ,dim2) :element-type ',type :initial-element ,val))

(defmacro vref (vector pos &optional value)
  (let ((g (gensym)))
    `(let ((,g ,value))
       (if ,g
           (setf (aref ,vector ,pos) ,g)
           (aref ,vector ,pos)))))

(defmacro chvar (sym comp predicate)
  (let ((g (gensym)))
    `(let ((,g ,comp))
       (if (or (null ,sym) (not (funcall ,predicate ,sym ,g)))
           (setf ,sym ,g)))))

(defmacro chmax (sym comp &optional (predicate #'>))
  `(chvar ,sym ,comp ,predicate))

(defmacro chmin (sym comp &optional (predicate #'<))
  `(chvar ,sym ,comp ,predicate))

(defmacro defchangef (name op default-val)
  `(defmacro ,name (var &optional (val ,default-val))
     `(setq ,var (,',op ,val ,var))))

;;本体
(defun read1 (str)
  (cond
    ((char= (aref str 0) #\1) (1+ (read1 (subseq str 1))))
    (t 0)))

(defmacro aif (test then &optional else)
  `(let ((it ,test))
     (if it ,then ,else)))


(defun main()
  (let* ((s (read-line)) (k (read)) (one (read1 s)))
    (println
     (cond
       ((<= k one) 1)
       (t (aref s one))))))

#-swank(main)