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::{stdin, Read};

macro_rules! parse {
    ($iter: ident) => {
        $iter.next().unwrap().parse().unwrap()
    };
    ($iter: ident,2) => {
        (parse!($iter), parse!($iter))
    };
    ($iter: ident,3) => {
        (parse!($iter), parse!($iter), parse!($iter))
    };
    ($iter: ident,4) => {
        (parse!($iter), parse!($iter), parse!($iter), parse!($iter))
    };
    ($iter: ident, $n: ident) => {
        $iter.take($n).map(|e| e.parse().unwrap()).collect();
    };
}

fn main() {
    let mut s = String::new();
    stdin().read_to_string(&mut s).unwrap();
    let mut iter = s.split_whitespace();
    let n: Vec<usize> = iter
        .next()
        .unwrap()
        .chars()
        .map(|x| x.to_digit(10).unwrap() as usize)
        .collect();
    let mut k: usize = parse!(iter);
    let mut res = 0;
    for (i, &ni) in n.iter().enumerate() {
        let i = n.len() - i - 1;
        if k == 0 {
            res += 1;
            break;
        }
        if ni == 0 {
            continue;
        }
        res += f(i, k);
        if i != 0 {
            res += (ni - 1) * f(i, k - 1);
        } else {
            res += ni * f(i, k - 1);
        }
        k -= 1;
    }
    println!("{}", res);
}
fn f(i: usize, k: usize) -> usize {
    match k {
        0 => 1,
        1 => 9 * i,
        2 => 81 * i * (i - 1) / 2,
        3 => 729 * i * (i - 1) * (i - 2) / 6,
        _ => 0,
    }
}