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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Linq;
class Program
{
	static void Main(string[] args)
	{
		int maxNumber = int.Parse(Console.ReadLine());
        int shouldNonZeroCount = int.Parse(Console.ReadLine());
        int numberCount = 0;
      
        for (int i = 1; i <= maxNumber; i++) {
          int number = i;
          int nonZeroCount = 1;
          while (true) {
            if (number < 10) break;
            if (number % 10 > 0) {
              nonZeroCount++;
            }
            number /= 10;
          }
          if (shouldNonZeroCount == nonZeroCount) {
            numberCount++;
          }
        }
      
        Console.WriteLine(numberCount);
    }
}