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: Runtime Error)

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 digit = N.length();
		int MAX = digit+1;
		long[][] com = new long[MAX][MAX];
		for(int i = 0; i < MAX; i++)
			com[i][0] = 1;
		for(int i = 1; i < MAX; i++)
			for(int j = 1; j <= i; j++)
				com[i][j] = com[i-1][j-1] + com[i-1][j];
		long ans = com[digit-1][K]*(long)Math.pow(9, K);
		ans += (Character.getNumericValue(N.charAt(0))-1) * com[digit-1][K-1] * (long)Math.pow(9, K-1);
		if(K == 1)
			ans++;
		else if(K == 2) {
			for(int i = 1; i < digit; i++) {
				int x = Character.getNumericValue(N.charAt(i));
				if(x != 0) {
					ans += x;
					ans += (digit-i-1)*9;
					break;
				}
			}
		}
		else {
			for(int i = 1; i < digit; i++) {
				int x = Character.getNumericValue(N.charAt(i));
				if(x != 0) {
					ans += com[digit-i-1][2] * 9 * 9;
					ans += (x-1) * (digit-i-1) * 9;
					for(int j = i+1; j < digit; j++) {
						int y = Character.getNumericValue(N.charAt(j));
						if(y != 0) {
							ans += y;
							ans += (digit-j-1) * 9;
							break;
						}
					}
				break;
				}		
			}
		}
		System.out.println(ans);

	}

}