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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let n: String = read();
    let k: usize = read();
    let mut dp = vec![vec![vec![0i64; 4]; 2]; n.len() + 1];
    dp[0][0][0] = 1; // pos, less, no_nontimes

    for (i, c) in n.chars().enumerate() {
        for j in 0..2 {
            for m in 0..4 {
                let lim = if j == 1 { 9 } else { c.to_digit(10).unwrap() };
                for l in 0..lim + 1 {
                    let idx1 = if j == 1 || l < lim { 1 } else { 0 };
                    let idx2;

                    if l != 0 {
                        idx2 = m + 1;
                    } else {
                        idx2 = m;
                    }
                    if idx2 > 3 {
                        continue;
                    }

                    dp[i + 1][idx1][idx2] += dp[i][j][m];
                }
            }
        }
    }
    // debug!(dp[0]);
    //  debug!(dp[n.len()]);

    let mut ans = 0;
    for j in 0..2 {
        ans += dp[n.len()][j][k];
    }
    println!("{:?}", ans);
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}