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: Runtime Error)

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

fn comb(n: u64, k: u64) -> u64 {
    if n < k {
        return 0;
    }
    if n == k {
        return 1;
    }
    let mut r = 1u64;
    for i in (n - k + 1)..(n + 1) {
        r *= i as u64;
    }
    // println!("   comb {} {} {}", n, k, r);
    for i in 1..(k + 1) {
        r /= i
    }
    // println!("   comb xxx {}", r);
    return r;
}

fn main() {
    input! {
        n: String,
        k: usize
    };

    let head = str::parse::<i64>(&n[0..k]).unwrap();
    let mut r = 0u64;

    let k = k as u64;

    for i in 0..head {
        let nonzero = i.to_string().chars().filter(|&x| x != '0').count();
        // println!("--- {} {} {}", i, nonzero, r);

        if nonzero == 0 { // 全部ゼロ
            // println!("B {} {}", comb(n.len() as u64 - k, k), 9u64.pow(k as u32));
            r += comb(n.len() as u64 - k, k) * 9u64.pow(k as u32);
        } else if nonzero == k as usize { // 全部非ゼロ
            // println!("C");
            r += 1;
        } else {
            // println!("D {} {}", comb(n.len() as u64 - k, k - nonzero as u64), 9u64.pow((k - nonzero as u64) as u32));
            r += comb(n.len() as u64 - k, k - nonzero as u64) * 9u64.pow((k - nonzero as u64) as u32);
        }
    }

    println!("{}", r + 1);
}
*/

fn main() {
    let exe = "/tmp/bin8C84190E";
    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>";