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"
#pragma GCC optimize("Ofast")

// Begin {{{
using namespace std;

#ifndef DEBUG
#define dump(...)
#endif

template <class A, class B> inline bool chmax(A &a, const B &b) noexcept {
    return b > a && (a = b, true);
}

template <class A, class B> inline bool chmin(A &a, const B &b) noexcept {
    return b < a && (a = b, true);
}

template <class T>
inline vector<T> make_v(const T &initializeValue, size_t sz) {
    return vector<T>(sz, initializeValue);
}

template <class T, class... Args>
inline auto make_v(const T &initializeValue, size_t sz, Args... args) {
    return vector<decltype(make_v<T>(initializeValue, args...))>(sz, make_v<T>(initializeValue, args...));
}

constexpr int INF = 0x3f3f3f3f;
constexpr int64_t LINF = 0x3f3f3f3f3f3f3f3fLL;
// }}} End

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    string S; intmax_t K;
    cin >> S >> K;

    size_t one = 0;
    for (const auto e : S) {
        if (e == '1') one++;
        else break;
    }
    dump(one);

    if (S.length() == 1) {
        return cout << S.front() << "\n", 0;
    }

    if (K <= one) {
        cout << 1 << "\n";
    } else {
        cout << S[one] << "\n";
    }

    return 0;
}