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)

fn read_stdin() -> String {
    use std::io::Read;
    let mut input = String::new();
    std::io::stdin().read_to_string(&mut input).unwrap();
    input
}

fn scan<'a, I: Iterator<Item = &'a str>, T: std::str::FromStr>(tokens: &mut I) -> T {
    tokens.next().unwrap().parse().ok().unwrap()
}

fn main() {
    let input = read_stdin();
    let tokens = &mut input.split_whitespace();
    let n: String = scan(tokens);
    let k: usize = scan(tokens);
    let n: Vec<usize> = n
        .chars()
        .map(|c| (c as i32 - '0' as i32) as usize)
        .collect();
    fn f(n: &[usize], k: usize) -> usize {
        if k == 0 {
            1
        } else if n.is_empty() {
            0
        } else if n[0] == 0 {
            f(&n[1..], k)
        } else {
            g(n.len() - 1, k) + (n[0] - 1) * g(n.len() - 1, k - 1) + f(&n[1..], k - 1)
        }
    }
    fn g(l: usize, k: usize) -> usize {
        let mut numer = 1;
        let mut denom = 1;
        for i in 0..k {
            numer *= l - i;
            numer *= 9;
            denom *= k - i;
        }
        numer / denom
    }
    println!("{}", f(&n, k));
}