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: Accepted)

class Main {
  public static void main(String[] args) {
    java.util.Scanner sc = new java.util.Scanner(System.in);
    String S = sc.next();
    long K = sc.nextLong();
    for (int i = 0; i < S.length(); i++) {
      switch (S.charAt(i)) {
        case '1':
          K -= 1;
          if (K > 0) continue;
          println('1');
          return;
        
        default:
          println(S.charAt(i));
          return;
      }
    }
  }

  /* 以下、標準出力用関数 */
  static public void print(byte what) { System.out.print(what); System.out.flush(); }
  static public void print(boolean what) { System.out.print(what); System.out.flush(); }
  static public void print(char what) { System.out.print(what); System.out.flush(); }
  static public void print(int what) { System.out.print(what); System.out.flush(); }
  static public void print(long what) { System.out.print(what); System.out.flush(); }
  static public void print(float what) { System.out.print(what); System.out.flush(); }
  static public void print(double what) { System.out.print(what); System.out.flush(); }
  static public void print(String what) { System.out.print(what); System.out.flush(); }
  static public void print(Object... variables) { StringBuilder sb = new StringBuilder(); for (Object o : variables) { if (sb.length() != 0) { sb.append(" "); } if (o == null) { sb.append("null"); } else { sb.append(o.toString()); } } System.out.print(sb.toString()); }
  static public void println() { System.out.println(); }
  static public void println(byte what) { System.out.println(what); System.out.flush(); }
  static public void println(boolean what) { System.out.println(what); System.out.flush(); }
  static public void println(char what) { System.out.println(what); System.out.flush(); }
  static public void println(int what) { System.out.println(what); System.out.flush(); }
  static public void println(long what) { System.out.println(what); System.out.flush(); }
  static public void println(float what) { System.out.println(what); System.out.flush(); }
  static public void println(double what) { System.out.println(what); System.out.flush(); }
  static public void println(String what) { System.out.println(what); System.out.flush(); }
  static public void println(Object... variables) { print(variables); println(); }
  static public void println(Object what) { if (what == null) { System.out.println("null"); } else if (what.getClass().isArray()) { printArray(what); } else { System.out.println(what.toString()); System.out.flush(); } }
  static public void printArray(Object what) { if (what == null) { System.out.println("null"); } else { String name = what.getClass().getName(); if (name.charAt(0) == '[') { switch (name.charAt(1)) { case '[': System.out.println(what); break; case 'L': Object poo[] = (Object[]) what; for (int i = 0; i < poo.length; i++) { if (poo[i] instanceof String) { System.out.println("[" + i + "] \"" + poo[i] + "\""); } else { System.out.println("[" + i + "] " + poo[i]); } } break; case 'Z': boolean zz[] = (boolean[]) what; for (int i = 0; i < zz.length; i++) { System.out.println("[" + i + "] " + zz[i]); } break; case 'B': byte bb[] = (byte[]) what; for (int i = 0; i < bb.length; i++) { System.out.println("[" + i + "] " + bb[i]); } break; case 'C': char cc[] = (char[]) what; for (int i = 0; i < cc.length; i++) { System.out.println("[" + i + "] '" + cc[i] + "'"); } break; case 'I': int ii[] = (int[]) what; for (int i = 0; i < ii.length; i++) { System.out.println("[" + i + "] " + ii[i]); } break; case 'J': long jj[] = (long[]) what; for (int i = 0; i < jj.length; i++) { System.out.println("[" + i + "] " + jj[i]); } break; case 'F': float ff[] = (float[]) what; for (int i = 0; i < ff.length; i++) { System.out.println("[" + i + "] " + ff[i]); } break; case 'D': double dd[] = (double[]) what; for (int i = 0; i < dd.length; i++) { System.out.println("[" + i + "] " + dd[i]); } break; default: System.out.println(what); } } else { System.out.println(what); } } System.out.flush(); }
}