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 static System.Math;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            A();
        }

        static void A()
        {
            var S = Read().ToList();
            var K = ReadLong();

            if (S.Count == 1 || K == 1 || (S.Count > 1 && S[0] != '1'))
            {
                Println(S[0]);
            }
            else if (S.Count(x => x != '1') == 0 || S.FindIndex(x => x != '1') + 1 > K)
            {
                Println(1);
            }
            else
            {
                Println(S[S.FindIndex(x => x != '1')]);
            }
        }

        static IEnumerable<int> Range(int start, int stop)
        {
            if (start < 0 || stop < 0 || start > stop || (start <= 0 && stop <= 0))
                return new List<int>();

            return Enumerable.Range(start, stop - start);
        }

        static bool IsDigit(string str)
        {
            var i = 0;
            return int.TryParse(str, out i);
        }

        static int DigitsSum(long num)
        {
            return num.ToString().Select(x => x.ToString()).Sum(int.Parse);
        }

        static int[] ToIntArray(string str)
        {
            return str.Select(x => x.ToString()).Select(int.Parse).ToArray();
        }

        static int Gcd(int a, int b) => b == 0 ? a : Gcd(b, a % b);

        static bool IsPrime(int x)
        {
            if (x <= 1 || (x != 2 && x % 2 == 0)) return false;
            if (x == 2) return true;

            for (int i = 3; i < x; i += 2)
                if (x % i == 0) return false;

            return true;
        }

        static string Read() => Console.ReadLine();
        static int ReadInt() => int.Parse(Read());
        static long ReadLong() => long.Parse(Read());

        static List<string> ReadSplit() => Read().Split().ToList();
        static List<int> ReadSplitInt() => Read().Split().Select(int.Parse).ToList();
        static List<long> ReadSplitLong() => Read().Split().Select(long.Parse).ToList();

        static void Print(object value) => Console.Write(value.ToString());
        static void Println(object value) => Console.WriteLine(value.ToString());

        static string Join<T>(IEnumerable<T> list) => string.Join("", list);
    }

    public static class MyExtensions
    {
        public static string Slice(this string str, int start = 0, int stop = 0)
        {
            if (start > str.Length || stop > str.Length || start < 0 || stop < 0)
                return "";

            if (stop == 0) stop = str.Length;
            return str.Substring(start, stop - start);
        }
    }
}