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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Numerics;
using System.Linq;
using System.Collections.Generic;


namespace debug
{
    class Program
    {
        static void Main(string[] args)
        {
            ProgramC a = new ProgramC();
            a.main();

        }
    }

    //ABC096
    class ProgramA
    {
        public void main()
        {
            string[] s = Console.ReadLine().Split(' ');
            int a = int.Parse(s[0]);
            int b = int.Parse(s[1]);

            Console.WriteLine((a -1)*(b-1));
        }
    }

    class ProgramB
    {
        public void main()
        {
            int n = int.Parse(Console.ReadLine());

            int ans = 0;
            for (int i = 1; i <= n; i = i + 2)
            {
                int count = 0;
                for (int j = 1; j < Math.Sqrt(i);j++)
                {
                    if(i % j == 0)
                    {
                        if (i == j * j)
                            count++;
                        else
                            count += 2;
                    }
                }

                if (count == 8)
                    ans++;
            }

            Console.WriteLine(ans);
            

        }
    }

    class ProgramC
    {
        public void main()
        {
            string s = Console.ReadLine();
            long k = long.Parse(Console.ReadLine());

            int pos = 0;
            for(int i = 0;i < s.Length;i++)
            {
                if (s[i] != '1')
                {
                    pos = i;
                    break;
                }
            }

            if (k - 1 < pos)
                Console.WriteLine("1");
            else
                Console.WriteLine(s[pos]);

        }
    }

    class ProgramD
    {
        public void main()
        {
            long n = long.Parse(Console.ReadLine());
            string[] xi = Console.ReadLine().Split(' ');

            long[] a = new long[n];

            for (int i = 0; i < n; i++)
                a[i] = long.Parse(xi[i]);

            //ソートする
            Array.Sort(a);

            //最大値候補
            long sum = a[n - 1] / 2;

            //二分探索
            long min = -1;
            long max = n;
            while(min + 1 != max)
            {
                long temp = (min + max) / 2;
                if (a[temp] <= sum)
                    min = temp;
                else
                    max = temp;
            }

            if(min == -1)
            {
                Console.WriteLine(a[n - 1] + " " + a[0]);
                return;
            }

            if (min == n - 2)
            {
                Console.WriteLine(a[n - 1] + " " + a[n - 2]);
                return;
            }

            if (sum - a[min] < a[max] - sum)
                Console.WriteLine(a[n - 1] + " " + a[min]);
            else
                Console.WriteLine(a[n - 1] + " " + a[max]);

        }

    }

    

}