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 <bits/stdc++.h>
#define pb push_back
#define rep(i,n) for(int i = 0;i < (n); ++i)
#define all(v) sort(v.begin(),v.end())
#define ALL(v) sort(v.begin(),v.end(),greater<ll>())
typedef long long ll;
typedef long double la;
using namespace std;

int main(){
    string s;
    ll k;
    cin >> s >> k;
    ll infinity = 500000000000000;
    if(s.size() == 1){
        cout << s << endl;
        return 0;
    }
    if(s[0] == '1'){
        if(k == 1){
            cout << s[0] << endl;
            return 0;
        }
        rep(i,s.size()){
            if(s[i] != '1'){
                cout << s[i] << endl;
                return 0;
            }
        }
    }
    if(s[0] != '1'){
        cout << s[0] << endl;
        return 0;
    }
    
}