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;
typedef long long ll;
#define _overload3(_1,_2,_3,name,...) name
#define _rep(i,n) repi(i,0,n)
#define repi(i,a,b) for(ll i=ll(a);i<ll(b);++i)
#define rep(...) _overload3(__VA_ARGS__,repi,_rep,)(__VA_ARGS__)
#define inf (ll)1e9
#define mod (ll)(1e9+7)
#define d(x) cerr<<#x<<"="<<x<<endl;
#define p(x) cout<<(x)<<endl
#define ps(x) cout<<(x);
#define pfix(d,x) cout << fixed << setprecision(d) << x << endl;
#define pb push_back
#define all(v) (v).begin(), (v).end()
#define minel(v) *min_element(all(v))
#define minind(v) distance((v).begin(), min_element(all(v)))
#define maxel(v) *max_element(all(v))
#define maxind(v) distance((v).begin(), max_element(all(v)))
#define fi first
#define se second
ll a,b,c,d,n,m,p,q,x,y,k,h,w,sum,mi,ma,ans,l,r,res;
string s;
typedef vector<int> VI;
typedef vector<pair<int,int> > VP;

int main() {
    cin>>s>>k;
    rep(i,s.size()){
        if(s[i]!='1'){p(s[i]);break;}
        if(i==k-1){p(s[i]);break;}
    }
    return 0;
}