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: Accepted)

import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        char[] n = sc.next().toCharArray();
        int k = sc.nextInt();
        int[] a = new int[n.length+1];
        for (int i = 0; i < n.length; i++) {
            a[i+1] = (int)(n[i] - '0');
        }
        long[][] dp1 = new long[a.length][k+1];
        long[][] dp2 = new long[a.length][k+1];
        dp2[0][0] = 1;
        for (int i = 1; i < a.length; i++) {
            if(a[i] == 0){
                for (int j = 0; j <= k; j++) {
                    dp1[i][j] += dp1[i-1][j];
                    dp2[i][j] += dp2[i-1][j];
                    if(0<j){
                        // set any
                        dp1[i][j] += dp1[i-1][j-1] * 9;
                    }
                }
            }else{
                for (int j = 0; j <= k; j++) {
                    // set 0
                    dp1[i][j] += dp1[i-1][j] + dp2[i-1][j];
                    if(0 < j){
                        // set max
                        dp2[i][j] += dp2[i-1][j-1];
                        // set any
                        dp1[i][j] += dp1[i-1][j-1] * 9 + dp2[i-1][j-1] * (a[i]-1);
                    }
                }
            }
        }
        System.out.println(dp1[a.length-1][k] + dp2[a.length-1][k]);
        sc.close();

    }

}