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)

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 f(nv: Vec<u32>, k: u32) -> u32 {
    let mut ret;
    let l = nv.len() as u32;

    // println!("nv : {:?}, k : {}", nv, k);

    if k == 1 {
        if l < 1 {
            ret = 0;
        } else {
            ret = nv[0] + (nv.len() as u32 - 1) * 9;
        }
    } else if k == 2 {
        if l < 2 {
            ret = 0;
        } else {
            let mut mv = vec![];
            let mut b = false;
            for i in 1..l as usize {
                if !b {
                    if nv[i] != 0 {
                        b = true;
                        mv.push(nv[i]);
                    }
                } else {
                    mv.push(nv[i]);
                }
            }
            ret = f(mv, k - 1);
            ret += (nv[0] - 1) * 9 * (l as u32 - 1);
            ret += 9 * 9 * (l - 1) * (l - 2) / 2;
        }
    } else {
        if l < 3 {
            ret = 0;
        } else {
            let mut mv = vec![];
            let mut b = false;
            for i in 1..l as usize {
                if !b {
                    if nv[i] != 0 {
                        b = true;
                        mv.push(nv[i]);
                    }
                } else {
                    mv.push(nv[i]);
                }
            }
            ret = f(mv, k - 1);
            ret += (nv[0] - 1) * 9 * 9 * (l - 1) * (l - 2) / 2;
            ret += 9 * 9 * 9 * (l - 1) * (l - 2) * (l - 3) / 6;
        }
    }

    ret
}

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

    println!("{}", f(nv, k));
}