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: Wrong Answer)

pub 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()
}

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

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

fn main() {
    let s: String = read();
    let k: u32 = read();
    let l = s.len() as u32;
    let nv: Vec<u32> = s.chars().map(|c| c as u32 - '0' as u32).collect();

    let ans;
    if k == 1 {
        let a = nv[0];

        ans = a + 9 * (l - 1);
    } else if k == 2 {
        if l < 2 {
            ans = 0;
        } else {
            let a = nv[0];
            let b = nv[1];

            if l == 2 {
                ans = b + (a - 1) * 9;
            } else {
                ans = b + 9 * (l - 2) + (a - 1) * 9 * (l - 1) + 81 * (l - 1) * (l - 2) / 2;
            }
        }
    } else {
        if l < 3 {
            ans = 0;
        } else {
            let a = nv[0];
            let b = nv[1];
            let c = nv[2];

            if l == 3 {
                ans = c + (b - 1) * 9 * (a - 1) * 81 * (l - 1) * (l - 2) / 2;
            } else {
                ans = c
                    + 9 * (l - 3)
                    + (b - 1) * 9 * (l - 2)
                    + 81 * (l - 2) * (l - 3) / 2
                    + (a - 1) * 81 * (l - 1) * (l - 2) / 2
                    + 729 * (l - 1) * (l - 2) * (l - 3) / 6;
            }
        }
    }

    println!("{}", ans);
}