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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String n = sc.next();
        int k = sc.nextInt();

        int digits = n.length();

        int[] digit = new int[digits];
        int second = 0;
        int third = 0;
        long ans = 0;

        for(int i = 0 ; i < digits ; i++){
            digit[i] = Integer.valueOf(n.substring(i, i+1));
            if(i > 0 && digit[i] > 0){
                if(second == 0) {
                    second = i;
                }else if(third == 0){
                    third = i;
                }
            }
        }

        System.out.println(count(n, k));
    }

    static long count(String n, int k){
        int digits = n.length();

        int[] digit = new int[digits];
        int second = 0;

        long ans = 0;

        for(int i = 0 ; i < digits ; i++){
            digit[i] = Integer.valueOf(n.substring(i, i+1));
            if(i > 0 && digit[i] > 0){
                if(second == 0) {
                    second = i;
                }
            }
        }

        if(k == 1){
            return 9*(digits-1) + digit[0];
        }else if(k == 2){
            ans += 81 * (digits - 2) * (digits - 1) / 2;
            ans += 9 * (digits - 1) * (digit[0] - 1);
            return (ans + count(n.substring(second, digits), k-1));
        }else{
            ans += 729 * (digits - 3) * (digits - 2) * (digits - 1) / 6;
            ans += 81 * (digits - 2) * (digits - 1) * (digit[0] - 1) / 2;
            return(ans + count(n.substring(second, digits), k-1));
        }
    }
}