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 lib_competition::prelude::*;

fn solve(n: String, k: usize) -> u64 {
    if n.len() < k {
        return 0;
    }

    let mut dp = vec![vec![vec![0u64; 2]; 4]; n.len() + 1];
    // dp[i][m][a] =（上部 c 桁までみたとき 1~9 が m 個含まれ，
    //               上部 c 桁が n と一致する(a=1)もしくはしない(a=0)数の総数）

    dp[0][0][1] = 1;

    for (i, c) in n.char_indices() {
        let c = c.to_digit(10).unwrap() as u64;
        for m in 0..4 {
            dp[i + 1][m][0] = dp[i][m][0]
                + if 0 < m { dp[i][m - 1][0] * 9 } else { 0 }
                + dp[i][m][1] * if c == 0 { 0 } else { 1 }
                + if 0 < m { dp[i][m - 1][1] * (std::cmp::max(c, 1) - 1) } else { 0 };
            dp[i + 1][m][1] = if c == 0 {
                dp[i][m][1]
            } else {
                if 0 < m {
                    dp[i][m - 1][1]
                } else {
                    0
                }
            };
        }
    }

    // for i in 0..2 {
    //     for j in 0..4 {
    //         for k in 0..(n.len() + 1) {
    //             print!("{:>5} ", dp[k][j][i]);
    //         }
    //         println!("");
    //     }
    //     println!("--");
    // }

    return dp[n.len()][k][0] + dp[n.len()][k][1];
}

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

    println!("{}", solve(n, k));
}
*/

fn main() {
    let exe = "/tmp/binC1412215";
    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>";