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 itn int
#define nibu(K,x) binary_search(K.begin(),K.end(),x)
#define rep(i,n) for(ll i=0;i<n;i++)
#define all(x) x.begin(),x.end()
#define sz(x) x.size()
#define pb push_back
#define mp make_pair
#define Fi first
#define Se second
#define out(x) cout<<x<<endl
#define put(x) out(x)
#define in(x) cin>>x
#define maxx(a,b,c) max(a,max(b,c))
#define minn(a,b,c) min(a,min(b,c))
using ll = long long;
using vl = vector<ll>;
using vs = vector<string>;
const double pi = 3.14159265358979;
const ll mod = 1000000007;

int main() {
 string S;
  in(S);
  ll K;
  in(K);
  ll N =  sz(S);
  ll a=-100;
  rep(i,N){
   if(S[i]!='1'){
     a=i;
     break; 
   }
   }
  if(a<0) out(1);
 else if(K<=a) out(1);
  else out(S[a]);
}