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 AtcoderTemplateForCSharp
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var array = Console.ReadLine().ToArray();

            var k = long.Parse(Console.ReadLine());

            var list = new List<long>();

            for (int i = 0; i < array.Count(); i++)
            {
                if (i == 0)
                {
                    if (long.Parse(array[i].ToString()) == 1)
                    {
                        list.Add(1);
                    }
                    else
                    {
                        list.Add(long.Parse(array[i].ToString()) * 5000000000000000);
                    }
                }
                else
                {
                    if (long.Parse(array[i].ToString()) == 1)
                    {
                        list.Add(long.Parse(array[i - 1].ToString()) + 1);
                    }
                    else
                    {
                        list.Add(long.Parse(array[i - 1].ToString()) + long.Parse(array[i].ToString()) * 5000000000000000);
                    }
                }
            }

            for (int i = 0; i < list.Count(); i++)
            {
                if (k < list[i])
                {
                    Console.WriteLine(int.Parse(array[i].ToString()));
                    break;
                }
            }
        }
    }
}