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;
using System.Collections.Generic;
using System.Runtime.CompilerServices;
using System.IO;
using System.Linq;
using System.Runtime.InteropServices;
using System.Runtime.Remoting.Messaging;
using System.Security.Cryptography.X509Certificates;
using System.Security.Permissions;
using System.Text;
using static System.Console;
using static System.Math;
using static Ex;
class AC{
    /*------------------------------------------------------------------*/
    private string S;
    private long K;
    void Solve(){
        io.i(out S, out K);
        var oneChain = 0L;
        for(int i = 0; i < S.Length; ++i){
            if(S[i] == '1') { oneChain++; }
            else{
                break;
            }
        }
        if(K <= oneChain) { 1.Prt(); }
        else{ S.First(x => x != '1').Prt(); }
    }
    /*------------------------------------------------------------------*/
    void Test(){
        //--- TEST ---//
    }
    public static void Main(string[] args) => new AC().Stream();
    IO io = new IO();
    private void Stream(){
        /*
        var exStdIn = new System.IO.StreamReader("stdin.txt");
        SetIn(exStdIn);
        Test();
        */
        Solve();
        io.Flush();
    }
}
class IO{
    #region INPUT
    #region FastRead    
    private const int Size = 1 << 12;
    private readonly Stream _stream = OpenStandardInput();
    private readonly byte[] _buffer = new byte[Size];
    private int _ptr = 0, _buffLen = 0;
    private bool HasNextByte(){
        if(_ptr < _buffLen) return true;
        _ptr = 0;
        _buffLen = _stream.Read(_buffer, 0, Size);
        return _buffLen > 0;
    }
    private byte ReadByte(){
        if(HasNextByte()) return _buffer[_ptr++];
        else
        //inputの末尾の改行がないとerror
            throw new EndOfStreamException();
    }
    private bool IsAscii(int c) => '!' <= c && c <= '~';
    private char NextChar(){
        var b = ReadByte();
        while(!IsAscii(b)) b = ReadByte();
        return (char) b;
    }
    private string Next(){
        var sb = new StringBuilder();
        for(var b = NextChar(); IsAscii(b); b = (char) ReadByte()) sb.Append(b);
        return sb.ToString();
    }
    public string String => Next();
    public char Char => NextChar();
    public int Int => int.Parse(Next());
    public long Long => long.Parse(Next());
    public double Double => double.Parse(Next());
    #endregion
    #region LazyRead        
    private void scan<T>(ref T x){
        if(x is int) __refvalue(__makeref(x),int) = int.Parse(Next());
        else if(x is long) __refvalue(__makeref(x),long) = long.Parse(Next());
        else if(x is double) __refvalue(__makeref(x),double) = double.Parse(Next());
        else if(x is char) __refvalue(__makeref(x),char) = NextChar();
        else __refvalue(__makeref(x),string) = Next();
    }
    public void i<T>(out T t){
        t = default(T);
        scan(ref t);
    }
    public void i<T, TU>(out T t, out TU u){
        i(out t);
        i(out u);
    }
    public void i<T, TU, TV>(out T t, out TU u, out TV v){
        i(out t, out u);
        i(out v);
    }
    public void i<T, TU, TV, TW>(out T t, out TU u, out TV v, out TW w){
        i(out t, out u);
        i(out v, out w);
    }
    public void i<T, TU, TV, TW, TX>(out T t, out TU u, out TV v, out TW w, out TX x){
        i(out t, out u, out v);
        i(out w, out x);
    }
    public void i<T, TU, TV, TW, TX, TY>(out T t, out TU u, out TV v, out TW w, out TX x, out TY y){
        i(out t, out u, out v);
        i(out w, out x, out y);
    }
    public void ini<T>(out T[] a, int n){
        a = new T[n];
        for(int i = 0; i < n; ++i) i<T>(out a[i]);
    }
    public void ini<T, TU>(out T[] a, out TU[] b, int n){
        a = new T[n];
        b = new TU[n];
        for(int i = 0; i < n; ++i) i<T, TU>(out a[i], out b[i]);
    }
    public void ini<T, TU, TV>(out T[] a, out TU[] b, out TV[] c, int n){
        a = new T[n];
        b = new TU[n];
        c = new TV[n];
        for(var i = 0; i < n; ++i) i<T, TU, TV>(out a[i], out b[i], out c[i]);
    }
    public void ini<T>(out T[,] a, int h, int w){
        a = new T[h, w];
        for(int i = 0; i < h; ++i) for(int j = 0; j < w; ++j) i<T>(out a[i, j]);
    }
    #endregion
    #endregion
    #region OUTPUT
    private readonly StreamWriter _sw = new StreamWriter(OpenStandardOutput()){
#if DEBUG
        AutoFlush = true
#else
        AutoFlush = false
#endif
    };
    public void Flush() => Out.Flush();
    public void YN(bool f) => yn(f, "YES", "NO");
    public void Yn(bool f) => yn(f, "Yes", "No");
    public void yn(bool f, string y = "yes", string n = "no") => WriteLine(f ? y : n);
    #endregion
    public IO() { SetOut(_sw); }
}
static class Ex{
    #region マクロもどき      
    public static Dictionary<T1, T2> MERGE<T1, T2>(Dictionary<T1, T2> xs, Dictionary<T1, T2> ys) => xs.Except(xs.Join(ys, z => z.Key, z => z.Key, (a, b) => a)).Concat(ys).ToDictionary(z => z.Key, z => z.Value);
    public static void LOG<T>(T x, [CallerLineNumber] int line = 0) => Error.WriteLine($"--- LOG[{line}]: {x} ---");
    public static void FOR(int a, int b, Action<int> f) => FOR(a, b, 1, f);
    public static void FOR(int a, int b, int n, Action<int> f){
        for(int i = a; i < b; i += n) f(i);
    }
    public static void REP(int a, Action<int> f) => FOR(0, a, f);
    public static void REPEQ(int a, Action<int> f) => FOR(0, a + 1, f);
    public static void FOREQ(int a, int b, Action<int> f) => FOR(a, b + 1, f);
    public static void FOREQ(int a, int b, int n, Action<int> f) => FOR(a, b + 1, n, f);
    public static void REP(int a, int b, Action<int, int> f) => REP(a, i => REP(b, j => f(i, j)));
    public static void REP(int a, int b, int c, Action<int, int, int> f) => REP(a, i => REP(b, j => REP(c, k => f(i, j, k))));
    public static void REPEQ(int a, int b, Action<int, int> f) => REPEQ(a, i => REPEQ(b, j => f(i, j)));
    public static void REPEQ(int a, int b, int c, Action<int, int, int> f) => REPEQ(a, i => REPEQ(b, j => REPEQ(c, k => f(i, j, k))));
    public static T MIN<T>(params T[] xs) => xs.Min();
    public static T MAX<T>(params T[] xs) => xs.Max();
    public static IEnumerable<int> RANGE(int s, int e) => Enumerable.Range(s, e - s + 1);
    public static int LCM(int a, int b) => a * (b / GCD(a, b));
    public static int GCD(int a, int b) => (a < b) ? GCD(b, a) : b == 0 ? a : GCD(b, a % b);
    public static int LCM(params int[] xs) => xs.Aggregate(LCM);
    public static int GCD(params int[] xs) => xs.Aggregate(GCD);
    public static long LCM(long a, long b) => a * (b / GCD(a, b));
    public static long GCD(long a, long b) => (a < b) ? GCD(b, a) : b == 0L ? a : GCD(b, a % b);
    public static long LCM(params long[] xs) => xs.Aggregate(LCM);
    public static long GCD(params long[] xs) => xs.Aggregate(GCD);
    #endregion
    #region 拡張メソッド        
    public static void Rep(this int x, Action<int> f) => REP(x, f);
    public static void RepEq(this int x, Action<int> f) => REPEQ(x, f);
    public static int ToInt(this string s){
        double n;
        double.TryParse(s.TrimStart('0'), out n);
        return Convert.ToInt32(n);
    }
    public static int ToInt(this char c) => ToInt(c.ToString());
    public static int ToInt(this char[] c) => ToInt(new string(c));
    public static long ToLong(this string s){
        double n;
        double.TryParse(s.TrimStart('0'), out n);
        return Convert.ToInt64(n);
    }
    public static long ToLong(this int x) => (long) x;
    public static IEnumerable<long> ToLong(this IEnumerable<int> xs) => xs.Select(x => x.ToLong());
    public static long ToLong(this char c) => ToLong(c.ToString());
    public static long ToLong(this char[] c) => ToLong(new string(c));
    public static int ToMod(this int x, int mod = (int) (1e9 + 7)) => x % mod;
    public static long ToMod(this long x, long mod = (long) (1e9 + 7)) => x % mod;
    public static void Do<T>(this T x, Action<T> f) => f(x);
    public static TU Then<T, TU>(this T x, Func<T, TU> f) => f(x);
    public static void Fun<T>(this T[] xs, Action<int> f) => REP(xs.Length, f);
    public static void Fun<T>(this T[,] xxs, Action<int, int> f) => REP(xxs.GetLength(0), i => REP(xxs.GetLength(1), j => f(i, j)));
    public static bool IsIn<T>(this T[] xs, int i) => 0 <= i && i < xs.Length;
    public static bool IsIn<T>(this T[,] xxs, int i, int j) => 0 <= i && i < xxs.GetLength(0) && 0 <= j && j < xxs.GetLength(1);
    public static void Iter<T>(this IEnumerable<T> xs, Action<T> f){
        foreach(var x in xs) f(x);
    }
    public class IndexedItem<T>{
        public int Idx;
        public T Val;
        public IndexedItem(int idx, T val){
            Idx = idx;
            Val = val;
        }
    }
    public static IEnumerable<IndexedItem<T>> Indexed<T>(this IEnumerable<T> xs) => xs.Select((x, i) => new IndexedItem<T>(i, x));
    public static Dictionary<long, int> PrimeFactor(this int x) => ((long) x).PrimeFactor();
    public static Dictionary<long, int> PrimeFactor(this long n){
        var ret = new Dictionary<long, int>();
        for(var i = 2; i <= n; ++i){
            if(!ret.ContainsKey(i)) ret[i] = 0;
            while(n % i == 0){
                ++ret[i];
                n /= i;
            }
        }
        return ret.Where(kp => kp.Value != 0).ToDictionary(kp => kp.Key, kp => kp.Value);
    }
    public static void Set<T>(this T[] xs, T v) => REP(xs.Length, i => xs[i] = v);
    public static void Set<T>(this T[,] xxs, T v) => REP(xxs.GetLength(0), i => REP(xxs.GetLength(1), j => xxs[i, j] = v));
    public static T[] Sort<T>(this T[] xs){
        Array.Sort(xs);
        return xs;
    }
    public static T[] SortR<T>(this T[] xs){
        Array.Reverse(xs.Sort());
        return xs;
    }
    public static string Pad0<T>(this T s, int n) => s.ToString().PadLeft(n, '0');
    public static int RoundOff(this double v, int n) => (int) Round(v, n - 1, MidpointRounding.AwayFromZero);
    public static int RoundUp(this double v) => (int) Ceiling(v);
    public static int RoundDown(this double v) => (int) Floor(v);
    public static bool Odd(this int v) => (v & 1) != 0;
    public static bool Odd(this long v) => (v & 1) != 0;
    public static bool Eve(this int v) => !v.Odd();
    public static bool Eve(this long v) => !v.Odd();
    public static void Prt<T>(this T x) => WriteLine(x);
    public static void Prt<T>(this T[] xs) => xs.Iter(x => WriteLine(x));
    public static void Prt<T>(this List<T> xs) => xs.Iter(x => WriteLine(x));
    public static void Prt<T>(this T[,] xs) => xs.GetLength(0).Rep(i =>{
        xs.GetLength(1).Rep(j => Write($"{xs[i, j]} "));
        WriteLine();
    });
    public static void Prt_<T>(this T[] xs) => WriteLine(string.Join(" ", xs));
    public static void Log<T>(this T x, [CallerLineNumber] int line = 0){
#if DEBUG
        Error.WriteLine($"--- LOG[{line}]: {x} ---");
#endif
    }
    public static void Log<T>(this T[] xs, [CallerLineNumber] int line = 0){
#if DEBUG
        Error.WriteLine($"^^^ LOG[{line}] ^^^");
        xs.Iter(x => Error.WriteLine(x));
        Error.WriteLine($"vvv LOG[{line}] vvv\n");
#endif
    }
    public static void Log<T>(this T[,] xs, [CallerLineNumber] int line = 0){
#if DEBUG
        Error.WriteLine($"^^^ LOG[{line}] ^^^");
        xs.GetLength(0).Rep(i =>{
            xs.GetLength(1).Rep(j => Error.Write($"{xs[i, j]} "));
            Error.WriteLine();
        });
        Error.WriteLine($"vvv LOG[{line}] vvv\n");
#endif
    }
    public static string Reversed(this string s) => string.Join("", s.Reverse());
    public static string Repeat(this string s, int n) => string.Concat(Enumerable.Repeat(s, n).ToArray());
    #endregion
}