Problem:
Score : 500 points

Problem Statement

Find the number of integers between 1 and N (inclusive) that contains exactly K non-zero digits when written in base ten.

Constraints

1 \leq N < 10^{100}

1 \leq K \leq 3

Input

Input is given from Standard Input in the following format:

N
K

Output

Print the count.

Sample Input 1

100
1

Sample Output 1

19

The following 19 integers satisfy the condition:

1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100

Sample Input 2

25
2

Sample Output 2

14

The following 14 integers satisfy the condition:

11,12,13,14,15,16,17,18,19,21,22,23,24,25

Sample Input 3

314159
2

Sample Output 3

937

Sample Input 4

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
3

Sample Output 4

117879300

Solution in Rust (1.15.1) (judge verdict: Accepted)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
use proconio::marker::Bytes;

fn c(n: usize, k: usize) -> usize {
    return if k > n {
        0
    } else if k == 1 {
        n
    } else if k == 2 {
        n * (n - 1) / 2
    } else if k == 3 {
        n * (n - 1) * (n - 2) / 6
    } else {
        unreachable!()
    };
}

fn f(s: &Vec<usize>, i: usize, k: usize, l: bool) -> usize {
    if k == 0 {
        return 1;
    }
    if i == s.len() {
        return 0;
    }
    if l {
        return c(s.len() - i, k) * 9usize.pow(k as u32);
    }
    if s[i] == 0 {
        return f(s, i + 1, k, false);
    }
    return f(s, i + 1, k, true) // 0xxxxx
        + f(s, i + 1, k - 1, true) * (s[i] - 1) // (1-(d-1))xxxxx
        + f(s, i + 1, k - 1, false) // dxxxxx
        ;
}

fn main() {
    input! {
        mut s: Bytes,
        nzc: usize
    };
    let bs = s.into_iter().map(|b| (b - b'0') as usize).collect();
    let ans = f(&bs, 0, nzc, false);
    println!("{}", ans);
}
*/

fn main() {
    let exe = "/tmp/bin243FA7AC";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";