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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define INF 2147483647
#define INFF 9223372036854775807
#define ll long long
#define REP(i,n) for(long long i=0;i<n;i++)
#define REPP(i,m,n) for(long long i=m;i<n;i++)
#define ALL(N) (N.begin(),N.end())
#define de cout << "debug" << endl;
#define pb push_back
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const long long M = 5000000000000000;

int ctoi(const char c){
  if('0' <= c && c <= '9') return (c-'0');
  return -1;
}

int main() {
    cin.tie(0);    
	ios::sync_with_stdio(false);
    string S;
    cin >> S;
    ll K;
    cin >> K;
    ll ans = 0;
    REP(i,S.size()){
        ll cnt = 1;
        int num = ctoi(S[i]);
        if(num == 1){
            ans += 1;
            if(ans >= K){
                cout << num << endl;
                return 0;
            }
            continue;
        }
        REP(j,M){
            cnt *= num;
            if(ans + cnt >= K){
                cout << num << endl;
                return 0;
            }
        }
    }
}