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>
#include <iostream>
#include <sstream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <cctype>
#include <string>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <algorithm>
#include <functional>
using namespace std; 
#define DEBUG(x) cout << '>' << #x << ':' << x << endl;
#define REP(i,n) for(int i=0;i<(n);i++)
#define FOR(i,a,b) for(int i=(a);i<=(b);i++)
#define FORD(i,a,b) for(int i=(a);i>=(b);i--)
inline bool EQ(double a, double b) { return fabs(a-b) < 1e-9; }
const int INF = 1<<29;
typedef long long int ll;
inline int two(int n) { return 1 << n; }
inline int test(int n, int b) { return (n>>b)&1; }
inline void set_bit(int & n, int b) { n |= two(b); }
inline void unset_bit(int & n, int b) { n &= ~two(b); }
inline int last_bit(int n) { return n & (-n); }
inline int ones(int n) { int res = 0; while(n && ++res) n-=n&(-n); return res; }
template<class T> void chmax(T & a, const T & b) { a = max(a, b); }
template<class T> void chmin(T & a, const T & b) { a = min(a, b); }
const int MOD=1000000007;

bool isPowerOfTwo (ll x)  
{  
    return x && (!(x&(x-1)));  
}
bool isPrime(int n) 
{ 
    if (n <= 1)  return false; 
    if (n <= 3)  return true; 
    if (n%2 == 0 || n%3 == 0) return false; 
  
    for (int i=5; i*i<=n; i=i+6) 
        if (n%i == 0 || n%(i+2) == 0) 
           return false; 
  
    return true; 
}
int highestPowerof2(unsigned int n) 
{ 
    // Invalid input 
    if (n < 1) 
        return 0; 
  
    int res = 1;
    for (int i=0; i<8*sizeof(unsigned int); i++) 
    { 
        int curr = 1 << i; 
        if (curr > n) 
           break; 
  
        res = curr; 
    } 
  
    return res; 
} 
long long binpow(long long a, long long b) {
    long long res = 1;
    while (b > 0) {
        if (b & 1)
            res = res * a;
        a = a * a;
        b >>= 1;
    }
    return res;
}       
////////////////////////////////////////////////////////////////////

int main()
{
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);  
  cout.tie(NULL);
  ll t=1;
  while(t--)
  {
    string s;ll k;
    cin>>s>>k;
    ll ans;
    cout<<k;
    for(ll i=0;i<s.length();i++)
    {
        if(k==0)
        break;
        if(s[i]=='1')
        k--;
        else
        {
            ans=s[i]-'0';
            break;
        }
    }
    if(k)cout<<ans;
    else
    {
        cout<<1;
    }
    
  }  
  return 0;
}