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)

use std::io::{self, BufReader, Read};
use std::str::FromStr;
use std::string::String;

fn main() {
	let mut sc = ::Scanner::new(io::stdin());
	let s = sc.next_str().unwrap();
	let k = sc.next_as::<u64>().unwrap();
	let f = s.char_indices().skip_while(|c| c.1 == '1' ).next();
	if let Some(c) = f {
		println!("{}", if k <= c.0 as u64 { '1' } else { c.1 });
	} else {
		println!("{}", '1')
	}
}

#[derive(Debug)]
pub struct Scanner<R> {
	reader: BufReader<R>
}

impl<R: io::Read> Scanner<R> {
	
	pub fn new(read: R) -> Scanner<R> {
		Scanner { reader: BufReader::new(read) }
	}

	pub fn next_str(&mut self) -> Option<String> {
		let mut buf = [0; 1];
		let size = self.reader.read(&mut buf).unwrap();
		if size == 0 {
			None{}
		} else {
			let first = self.skip_whitespace(&mut buf);
			if first.is_none() {
				return None{}
			}
			let mut v = vec![buf[0]];
			loop {
				let size = self.reader.read(&mut buf).unwrap();
				if size == 0 || char::from(buf[0]).is_whitespace() {
					break;
				}
				v.push(buf[0]);
			}
			Some(String::from_utf8(v).unwrap())
		}
	}

	pub fn next_line(&mut self) -> Option<String> {
		let mut buf = [0; 1];
		let mut v :Vec<u8> = vec![];
		let mut size = self.reader.read(&mut buf).unwrap();
		if size == 0 {
			return None{}
		}
		loop {
			if size == 0 || char::from(buf[0]) == '\n' {
				return Some(String::from_utf8(v).unwrap())
			}
			v.push(buf[0]);
			size = self.reader.read(&mut buf).unwrap();
		}
	}

	pub fn next_vec<S: FromStr>(&mut self, size: u32) -> Vec<S> {
		let mut v: Vec<S> = vec![];
		for _ in 0..size {
			let token = self.next_str().unwrap();
			v.push(S::from_str(&token).ok().unwrap());
		}
		v
	}

	pub fn next_as<S: FromStr>(&mut self) -> Option<S> {
		if let Some(s) = self.next_str() {
			if let Ok(v) = S::from_str(&s) {
				return Some(v)
			}
		}
		None{}
	}

	pub fn next_i32(&mut self) -> Option<i32> {
		self.next_as::<i32>()
	}

	pub fn next_i64(&mut self) -> Option<i64> {
		self.next_as::<i64>()
	}

	pub fn next_f32(&mut self) -> Option<f32> {
		self.next_as::<f32>()
	}

	pub fn next_f64(&mut self) -> Option<f64> {
		self.next_as::<f64>()
	}

	fn skip_whitespace(&mut self, mut buf: &mut [u8]) -> Option<u8> {
		loop {
			if !char::from(buf[0]).is_whitespace() {
				return Some(buf[0])
			}
			let size = self.reader.read(&mut buf).unwrap();
			if size == 0 {
				return None{}
			}
		}
	}
}