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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector> 
#include <cmath>
#include <algorithm>
#include <set>
#include <string>
#include <map>
#include <cerrno>
#include <stdio.h>
#include <stdlib.h>
#include <cfenv>
#include <stack>
#include <math.h>
#include <iomanip>
#include <limits>
#include <queue>
#define ll long long int
#define pb push_back
#define mp make_pair

using namespace std;

int main(){

    string s;
    ll k;
    cin >> s >> k;

    vector<int> vec;

    for(int i=0;i<s.size();i++){
        vec.pb(s[i]-'0');
    }

    int j=0;

    while(true){
        if(j==vec.size()){
            cout << 1 << endl;
            return 0;
        }
        if(vec[j] != 1){
            break;
        }
        j++;
    }

    if(k==1){
        cout << vec[0];
    }
    else if(j>k){
        cout << 1 << endl;
    }
    else{
        cout << vec[j] << endl;
    }
    return 0;
}