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 main() {
    let mut buf = String::new();
    let nums: Vec<i32> = {
        std::io::stdin().read_line(&mut buf).unwrap();
        buf.trim()
            .chars()
            .map(|ch| ch as i32 - '0' as i32)
            .collect()
    };
    let k: i32 = {
        buf.clear();
        std::io::stdin().read_line(&mut buf).unwrap();
        buf.trim().parse().unwrap()
    };
    fn comb(n: i32, k: i32) -> i32 {
        let mut c = 1;
        for i in 0..k {
            c *= n - i;
        }
        for i in 0..k {
            c /= k - i;
        }
        for _ in 0..k {
            c *= 9;
        }
        c
    }
    fn rec(nums: &[i32], k: i32) -> i32 {
        if k == 0 {
            1
        } else if nums.is_empty() {
            0
        } else if nums[0] == 0 {
            rec(&nums[1..], k)
        } else {
            let mut ans = 0;
            let l = nums.len() as i32;
            if k < l {
                ans += comb(l - 1, k);
            }
            if k <= l {
                if nums[0] > 1 {
                    ans += (nums[0] - 1) * comb(l - 1, k - 1);
                }
                ans += rec(&nums[1..], k - 1);
            }
            ans
        }
    }
    println!("{}", rec(&nums, k));
}