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)

trait FromFragment: Sized {
    fn from_fragment(s: &str) -> Result<Self, String>;
}

impl FromFragment for String {
    fn from_fragment(s: &str) -> Result<String, String> { Ok(s.to_owned()) }
}

#[allow(unused_macros)]
macro_rules! impl_from_fragment {
    ( $( $t:ty )* ) => { $(
        impl FromFragment for $t {
            fn from_fragment(s: &str) -> Result<$t, String> {
                use std::str::FromStr;
                <$t>::from_str(s).map_err(|_| {
                    format!("cannot parse \"{}\" as {}", s, stringify!($t))
                })
            }
        }
    )* };
}

impl_from_fragment!(isize usize i8 u8 i16 u16 i32 u32 i64 u64 f64);

trait FromLine: Sized {
    fn from_line(line: &str) -> Result<Self, String>;
}

impl<T: FromFragment> FromLine for T {
    fn from_line(line: &str) -> Result<T, String> {
        T::from_fragment(line.trim_right_matches('\n'))
    }
}

impl<T: FromFragment> FromLine for Vec<T> {
    fn from_line(line: &str) -> Result<Vec<T>, String> {
        let mut result = Vec::new();
        for fragment in line.trim_right_matches('\n').split_whitespace() {
            match T::from_fragment(fragment) {
                Ok(v) => result.push(v),
                Err(msg) => {
                    return Err(format!(
                        "fragment {} of line \"{}\": {}",
                        result.len() + 1, line, msg
                    ))
                }
            }
        }
        Ok(result)
    }
}

#[allow(unused_macros)]
macro_rules! impl_from_line_for_tuples {
    ($t:ident $var:ident $count:expr) => ();
    ($t:ident $var:ident $count:expr; $($inner_t:ident $inner_var:ident $inner_count:expr);*) => {
        impl <$t: FromFragment, $($inner_t: FromFragment),*> FromLine for ($t, $($inner_t),*) {
            #[allow(unused_assignments)]
            fn from_line(line: &str) -> Result<( $t, $($inner_t),*), String> {
                let fragments: Vec<&str> =
                    line.trim_right_matches('\n').split_whitespace().collect();
                if fragments.len() != $count {
                    return Err(format!(
                        "line \"{}\" has {} fragments, expected {}",
                        line, fragments.len(), $count
                    ));
                }

                let mut iter = fragments.iter();
                let mut n = 1;
                let $var = <$t>::from_fragment(iter.next().unwrap())
                    .map_err(|msg| {
                        format!("fragment {} of line \"{}\": {}", n, line, msg)
                    })?;
                n += 1;
                $(
                    let $inner_var =
                        <$inner_t>::from_fragment(iter.next().unwrap())
                        .map_err(|msg| {
                            format!("fragment {} of line \"{}\": {}",
                                    n, line, msg)
                        })?;
                    n += 1;
                )*
                Ok(( $var, $($inner_var),* ))
            }
        }
        impl_from_line_for_tuples!($($inner_t $inner_var $inner_count);*);
    }
}

impl_from_line_for_tuples!(T4 x4 4; T3 x3 3; T2 x2 2; T1 x1 1);

#[allow(unused_macros)]
macro_rules! read {
    // Discard a line
    () => {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
    };

    // Get a FromLine
    ( $pat:pat = $t:ty ) => {
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).unwrap();
        let $pat = <$t>::from_line(&line).unwrap();
    };

    // Get FromFragment's
    ( $( $pat:pat = $t:ty ),+ ) => {
        read!(($($pat),*) = ($($t),*));
    };
}

#[allow(unused_macros)]
macro_rules! read_n {
    // Get FromLine's
    ( $( $pat:pat = $t:ty ),+ ) => {
        $(
            read!($pat = $t);
        )*
    }
}

#[allow(unused_macros)]
macro_rules! read_loop {
    ( $pat:pat = $t:ty; $block:block ) => {
        use std::io::BufRead;
        let stdin = std::io::stdin();
        for line in stdin.lock().lines() {
            let line = line.expect("read from stdin failed");
            let $pat = <$t>::from_line(&line).unwrap();
            $block
        }
    };

    ( $($pat:pat = $t:ty),* ; $block:block ) => {
        read_loop!(($($pat),*) = ($($t),*); $block);
    }
}

fn main() {
    read!(s = String);
    read!(k = u64);
    let c = match (1..).zip(s.chars()).find(|&(_, c)| c != '1') {
        None => '1',
        Some((n, c)) => if n <= k { c } else { '1' }
    };
    println!("{}", c);
}