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 Rust (1.15.1) (judge verdict: Accepted)

// https://atcoder.jp/contests/abc106/tasks/abc106_c

#[allow(unused)]
use std::cmp::{max, min, Ordering};
#[allow(unused)]
use std::collections::{HashSet, VecDeque};
use std::io;
use std::io::{BufRead, Read, Write};
use std::str::FromStr;

/* Input macro */

#[allow(unused)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[allow(unused)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused, non_snake_case)]
pub fn solve<R: BufRead, W: Write>(mut io: Io<R, W>) {
    let input = io.read_all();
    input! {
        source = input,
        S: chars,
        K: usize,
    }

    let res = S
        .into_iter()
        .take(K)
        .skip_while(|&c| c == '1')
        .next()
        .unwrap_or('1');

    io.println(res);
}

#[allow(dead_code)]
fn main() {
    let stdin = io::stdin();
    let stdin_lock = stdin.lock();
    let stdout = io::stdout();
    let stdout_lock = stdout.lock();

    let io = Io {
        reader: stdin_lock,
        writer: stdout_lock,
    };

    solve(io);
}

/* IO helpers */

pub struct Io<R, W>
where
    R: BufRead,
    W: Write,
{
    pub reader: R,
    pub writer: W,
}

#[allow(dead_code)]
impl<R, W> Io<R, W>
where
    R: BufRead,
    W: Write,
{
    fn println<T: std::fmt::Display>(&mut self, value: T) {
        writeln!(&mut self.writer, "{}", value).expect("Unable to write");
    }

    fn print<T: std::fmt::Display>(&mut self, value: T) {
        write!(&mut self.writer, "{}", value).expect("Unable to write");
    }

    fn debug<T: std::fmt::Debug>(&mut self, value: T) {
        writeln!(&mut self.writer, "{:?}", value).expect("Unable to write");
    }

    fn next<T: FromStr>(&mut self) -> T {
        let token = self
            .reader
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok().expect("Unable to parse")
    }

    fn nexts<T: FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.next::<T>()).collect::<Vec<T>>()
    }

    fn read_all(&mut self) -> String {
        let mut res = String::new();
        self.reader.read_to_string(&mut res).unwrap();
        res
    }
}

/* Structure helpers */

trait IteratorExt: Iterator + Sized {
    fn vec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

impl<T: Iterator> IteratorExt for T {}