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::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char) 
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn solve(s: String, K: usize) -> usize {
    let si: Vec<char> = s.chars().collect();

    let mut dp = vec![vec![vec![0; K+2]; 2]; s.len()+1];  // dp[決めた桁数][未満フラグ][対象カウント] := 総数
    dp[0][0][0] = 1;

    for i in 0..s.len() {
        let D: usize = (si[i] as usize) - ('0' as usize);
        for j in 0..2 {
            for k in 0..K+1 {
                for d in 0..10 {
                    if j == 0 && d > D {
                        break;
                    }
                    let is_smaller: usize = (j == 1 || d < D) as usize;
                    let count: usize;
                    if d == 0 {
                        count = k;
                    } else {
                        count = k + 1;
                    }
                    dp[i+1][is_smaller][count] += dp[i][j][k];
                }
            }
        }
    }

    return dp[s.len()][0][K] + dp[s.len()][1][K];
}

fn main() {
    let n: String = read();
    let k: usize = read();

    println!("{}", solve(n, k));
}