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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main
{

  public static final long LATER_DATE = 5000000000000000L;

  public static void main
  (
    String[] args
  )
  {
    BufferedReader in_stream;
    String         in_str;

    String in_S;
    long   in_K;


    int    cnt;
    String tmp;
    long   digit;
    String ans;

    try
    {
      in_stream = new BufferedReader(new InputStreamReader(System.in));

      /*----------------
       * 引数
       *----------------*/
      in_S   = new String(in_stream.readLine());

      in_str = new String(in_stream.readLine());
      in_K   = Long.parseLong(in_str);


      /*----------------
       * 計算
       *----------------*/
      ans = "1";
      digit = 1;
      for(cnt=0; cnt<in_S.length(); cnt++)
      {
        tmp = in_S.substring(cnt, cnt+1);
        if("1".equals(tmp))
        {
          /* Nothing to do. */
        }
        else
        {
          digit += (new Double(Math.ceil( LATER_DATE * Math.log10(Double.parseDouble(tmp)) ))).longValue();
        }

        if(in_K <= digit)
        {
          ans = tmp;
          break;
        }
      }

      System.out.println(ans);
    }
    catch(Exception e)
    {
      e.printStackTrace();
    }
  }
}