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)

use std::io::*;
use std::str::*;

fn read<T: FromStr>() -> Option<T> {
    let stdin = stdin();
    let s = stdin
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect::<String>();
    s.parse::<T>().ok()
}

fn solve(n: &str, k: usize) -> usize {
    if k == 0 {
        return 1;
    }
    if n.len() < k {
        return 0;
    }

    let top: usize = n[0..1].parse().unwrap();
    if top == 0 {
        solve(&n[1..], k)
    } else {
        let mut s = String::new();
        for _ in 0..(n.len() - 1) {
            s.push_str("9");
        }
        let mut ans = 0;
        //000000~099999
        ans += solve(&s, k);
        //100000~299999
        ans += (top - 1) * solve(&s, k - 1);
        //300000~314159
        ans += solve(&n[1..], k - 1);
        ans
    }
}

fn main() {
    let n: String = read().unwrap();
    let k: usize = read().unwrap();
    println!("{}", solve(&n, k));
}