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)

//! ----------------------------------------------
//! Framework <https://github.com/vain0x/procon>
//!
//! See the bottom of file for solution.
//! ----------------------------------------------

#![allow(unused_imports)]
#![allow(non_snake_case)]

use std::cell::RefCell;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::fmt::{Debug, Display, Formatter, Write as FmtWrite};
use std::io::{stderr, stdin, BufRead, Write};
use std::mem::{replace, swap};
use std::ops::*;
use std::rc::Rc;

/// Print values to standard error if debug mode.
#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), stderr());
            writeln!(err, "\x1B[33m{}\x1B[0m = {:?}", e, $e).unwrap()
        })*
    };
}

/// Read from standard input and parse each word.
/// - `read!(T, U, ..)` parses a line as a tuple of words.
/// - `read![[T]]` parses a line as an array of words.
/// - `read![..; N]` parses `N` lines, using `read!(..)` repeatedly.
#[allow(unused_macros)]
macro_rules! read {
    ([$t:ty] ; $n:expr) =>
        ((0..$n).map(|_| read!([$t])).collect::<Vec<_>>());
    ($($t:ty),+ ; $n:expr) =>
        ((0..$n).map(|_| read!($($t),+)).collect::<Vec<_>>());
    ([$t:ty]) =>
        (rl().split_whitespace().map(|w| w.parse().unwrap()).collect::<Vec<$t>>());
    ($($t:ty),*) => {{
        let buf = rl();
        let mut w = buf.split_whitespace();
        ($(w.next().unwrap().parse::<$t>().unwrap()),*)
    }};
}

/// Read a line from standard input.
#[allow(dead_code)]
fn rl() -> String {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();

    #[allow(deprecated)]
    buf.trim_right().to_owned()
}

// -----------------------------------------------
// Solution
// -----------------------------------------------

fn main() {
    let N = rl().chars().collect::<Vec<char>>();
    let K = read!(usize);

    let h = N.len();

    let d1 = (N.get(0).cloned().unwrap_or('0') as u8 - b'0') as usize;
    let d2 = (N.get(1).cloned().unwrap_or('0') as u8 - b'0') as usize;
    let d3 = (N.get(2).cloned().unwrap_or('0') as u8 - b'0') as usize;
    let mut s = 0;

    // 凡例
    // = : N の同じ桁に同じ数字
    // * : N の同じ桁の数字より小さい、1以上の数字
    // 99...00... (9がK個、全体でN桁) : N桁の中に1以上の数字がちょうどK個含まれる

    match K {
        1 => {
            // =00
            // *00
            s += d1;

            // 090
            s += (h - 1) * 9;
        }
        2 if h >= 2 => {
            // ==00
            // =*00
            s += d2;

            // =090
            s += (h - 2) * 9;

            // *900
            s += (d1 - min(d1, 1)) * (h - 1) * 9;

            // 0990
            s += ((h - 1) * (h - 2) / 2) * 9 * 9;
        }
        3 if h >= 3 => {
            if d2 >= 1 {
                // ===000
                // ==*000
                s += d3;

                // ==0900
                s += (h - 3) * 9;
            }

            // =*9000
            s += (d2 - min(d2, 1)) * (h - 2) * 9;

            // =09900
            s += ((h - 2) * (h - 3) / 2) * 9 * 9;

            // *99000
            s += (d1 - min(d1, 1)) * ((h - 1) * (h - 2) / 2) * 9 * 9;

            // 099900
            s += ((h - 1) * (h - 2) / 2 * (h - 3) / 3) * 9 * 9 * 9;
        }
        _ => {}
    }

    println!("{}", s)
}