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: Wrong Answer)

use std::cmp;
use std::collections::*;
use std::io::{self, Read};

const MOD: usize = 1000000007;

fn main() {
    let stdin = io::stdin();
    let mut sc = Scanner::new(stdin.lock());

    let s: String = sc.read().unwrap();
    let s: Vec<char> = s.chars().collect();
    let k: usize = sc.read().unwrap();

    let mut i: usize = 0;
    let mut ans = '\0';
    for c in s {
        ans = c;

        match c {
            '1' => i = i + 1,
            c => i = i + c.to_digit(10).unwrap() as usize * 5000000000000000,
        }

        if i > k {
            break;
        }
    }

    println!("{}", ans);
}

struct Scanner<R: Read> {
    reader: R,
}

impl<R: Read> Scanner<R> {
    fn new(reader: R) -> Scanner<R> {
        Scanner { reader: reader }
    }

    fn read<T: std::str::FromStr>(&mut self) -> Option<T> {
        self.reader
            .by_ref()
            .bytes()
            .map(|b| b.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>()
            .parse()
            .ok()
    }

    fn read_vec<T: std::str::FromStr>(&mut self, n: usize) -> Option<Vec<T>> {
        (0..n).map(|_| self.read()).collect()
    }

    fn read_vec2d<T: std::str::FromStr>(&mut self, m: usize, n: usize) -> Option<Vec<Vec<T>>> {
        (0..m).map(|_| self.read_vec(n)).collect()
    }

    fn read_board(&mut self, n: usize) -> Option<Vec<Vec<char>>> {
        (0..n)
            .map(|_| {
                self.read::<String>()
                    .map(|s| s.chars().collect::<Vec<char>>())
            })
            .collect()
    }
}