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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp15
{
    class Class254
    {
        static void Main()
        {
            string N = Console.ReadLine();
            int K = int.Parse(Console.ReadLine());

            var dp = new int[N.Length + 1, K + 1,2];
            dp[0, 0,0] = 1; //0は含めないので後で引く。

            for(int i = 0; i < N.Length; i++)
            {
                int num = N[i] - '0';
                for(int j = 0; j < K; j++)
                {
                    for(int k = 0; k < 10; k++)
                    {
                        for(int l = 0; l < 2; l++)
                        {
                            int nl = l;
                            int nj = j;
                            if (l == 0)
                            {
                                if (k > num) continue;
                                if (k < num) nl = 1;
                            }
                            if (k != 0)
                            {
                                nj++;
                            }

                            dp[i + 1, nj, nl] += dp[i, j, l];
                        }
                    }
                }
            }

            int sum = 0;
            for(int i = 1; i <= N.Length; i++)
            {
                sum += dp[i, K,0]+dp[i,K,1];
            }
            Console.WriteLine(sum);
        }
    }
}