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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication16
{
    class Program
    {
        static void Main(string[] args)
        {
            //10の18乗より、2の5兆-1乗の方が大きい。
            //そのため、1が入ってこなければ、最初に指定された数字がK番目の文字となる。
            //頭に「1」が入っていて、その数字より下のK番目が指定された場合は「1」となる。
            //
            // Ex: 
            //  111222 
            //  3
            //  Ans:1
            //
            // Ex: 
            //  111222 
            //  4
            //  Ans:2
            // 答えが「1」になる条件
            // ・文字列Sの最初に出てくる「1」が100番目以下
            // ・Kが100以下
            // ・

            string S = Console.ReadLine();
            string K = Console.ReadLine();

            int cnt;
            string ret = "";
            for (cnt = 1; cnt < S.Length-1; cnt++)
            {
                string diff = S.Substring(cnt - 1, 1);
                if (diff != "1")
                {
                    if ((cnt <= 100) && K.Length <= 3 && (int.Parse(K) <= cnt))
                        ret = "1";
                    else
                        ret = diff;
                    break;
                }
            }
            Console.WriteLine(ret);
        }
    }
}