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: Accepted)

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

namespace AtCoder
{
    static class Program
    {
        static void Main()
        {
            //ここから

            string S = IO.ReadLineToString();
            long K = IO.ReadLineToLong();

            string ans = "1";
            for (var i = 0; i < Math.Min(99, K); i++)
            {
                if (S[i] != '1')
                {
                    ans = S[i].ToString();
                    break;
                }
            }

            //ここまで

            Console.WriteLine(ans);
            Console.ReadKey();
        }

    }

    static class Func
    {
        static long mod = 1000000007;
        static public void Swap<T>(ref T a, ref T b) { T temp = a; a = b; b = temp; }
        static public long GCD(long a, long b) { return b != 0 ? GCD(b, a % b) : a; }
        static public long LCM(long a, long b) { return (long)a * b / GCD(a, b); }
        static public int Factorial(int a) { return a == 1 ? a : a * Factorial(a - 1); }


        public static double ToAngle(this double radian)
        {
            return (double)(radian * 180 / Math.PI);
        }

        public static double ToRadian(this double angle)
        {
            return (double)(angle * Math.PI / 180);
        }

        static public long Conbination(int n,int m)
        {
            if (m == 0) return 1;
            if (n == 0) return 0;
            return n * Conbination(n - 1, m - 1) / m;
        }

        static public void Factoring(long num, ref long[] vs)
        {
            if (num == 1)
            {
                vs[1]++;
            }
            for (long i = 2; i < Math.Sqrt(num); i++)
            {
                if (num % i == 0)
                {
                    vs[i]++;
                    Factoring(num / i, ref vs);
                }
            }
            vs[1]++;
        }
    }

    static class IO
    {
        static public string ReadLineToString() { return Console.ReadLine(); }
        static public int ReadLineToInt() { return int.Parse(Console.ReadLine()); }
        static public long ReadLineToLong() { return long.Parse(Console.ReadLine()); }
        static public List<string> ReadLineToStringList() { return Console.ReadLine().Split(' ').ToList(); }
        static public List<int> ReadLineToIntList() { return Console.ReadLine().Split(' ').Select(int.Parse).ToList(); }
        static public List<long> ReadLineToLongList() { return Console.ReadLine().Split(' ').Select(long.Parse).ToList(); }

        static public List<double> ReadLineToDoubleList() { return Console.ReadLine().Split(' ').Select(double.Parse).ToList(); }

        static public void WriteStrings(object[] strings) { foreach (var o in strings) { Console.Write(o + " "); } }
    }
}