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: Time Limit Exceeded)

import java.math.BigInteger;
import java.util.Scanner;

/**
 * TITLE : Almost Everywhere Zero
 * URL : https://atcoder.jp/contests/abc154/tasks/abc154_e
 */
public class Main {
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		String N = sc.next();
		int K = sc.nextInt();
		int count = 0;

		for (BigInteger bi = new BigInteger(N);
	            bi.compareTo(BigInteger.ZERO) > 0;
	            bi = bi.subtract(BigInteger.ONE)) {
			String target = bi.toString();
			if (target.replace("0", "").length() == K) {
				count++;
			}
		}
		System.out.println(count);
		sc.close();
	}
}