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: Wrong Answer)

using System;
using System.Linq;

namespace PracticeForAtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            //ここから
            string n = Console.ReadLine();
            int k = int.Parse(Console.ReadLine());

            int ans = Solve(n, k);

            Console.WriteLine(ans);
            //ここまで
        }

        static int ncr(int n, int r)
        {
            int temp = 1;
            int bunbo = 1;
            for (int i = 1; i <= r; i++)
            {
                temp *= (n - i + 1);
                bunbo *= i;
            }

            return temp / bunbo;
        }
        static int Ketain(int ketasuu, int k)
        {
            return ncr(ketasuu, k) * (int)Math.Pow(9, k);
        }

        static int Solve(string n, int k)
        {
            int ans = 0;
            int length = n.Length;
            if (length < k) return 0;

            if (length > k)     ans += Ketain(length - 1, k);
            if (k > 1)
            {
                ans += Ketain(length - 1, k - 1) * (n[0].ToInt() - 1);
                ans += Solve(n.Remove(0, 1), k - 1);
            }
            if (k == 1) ans += n[0].ToInt();

            return ans;
        }

        

    }
    public static class CharExt
    {
        public static int ToInt(this char self)
        {
            return self - '0';
        }
    }

}