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 {

    private static char[] N;
    private static int K;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = sc.next().toCharArray();
        K = sc.nextInt();
        int[][][] dp = new int[N.length+1][K+1][2];
        dp[0][0][1] = 1;
        for (int i = 0; i < N.length; i++) {
            for (int j = 0; j <= K; j++) {
                for (int s = 0; s < 2; s++) {
                    if (dp[i][j][s] == 0)  continue;
                    if (s == 0) {
                        dp[i+1][j][0] = dp[i+1][j][0]+dp[i][j][0];
                        if (j+1 <= K) {
                            dp[i+1][j+1][0] = dp[i+1][j+1][0]+9*dp[i][j][0];
                        }
                    } else {
                        int a = N[i]-'0';
                        if (a == 0) {
                            dp[i+1][j][1] = dp[i+1][j][1]+dp[i][j][1];
                        } else {
                            dp[i+1][j][0] = dp[i+1][j][0]+dp[i][j][1];
                            if (j+1 <= K) {
                                dp[i+1][j+1][0] = dp[i+1][j+1][0]+(a-1)*dp[i][j][1];
                                dp[i+1][j+1][1] = dp[i+1][j+1][1]+dp[i][j][1];
                            }
                        }
                    }
                }
            }
        }
        System.out.println(dp[N.length][K][0]+dp[N.length][K][1]);
    }
}