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;

class Program
{
    static void Main(string[] args)
    {
        var N = long.Parse(Console.ReadLine());
        var K = int.Parse(Console.ReadLine());
        // var N = long.Parse("100");
        // var K = int.Parse("1");

        var cnt = 0;
        for (int i = 1; i <= N; i++)
        {
            var n = i.ToString().Replace("0", "").Length;
            var match = n == K;
            if (match) cnt++;

            Console.WriteLine($"{i}({n}) : {match}");
        }

        Console.WriteLine(cnt);
    }
}