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;
class ProgramE
    {
        static void Main(string[] args)
        {
            
            //入力
            string n = Console.ReadLine();
            int k = int.Parse(Console.ReadLine());

            int keta = n.Length;
            int sum = 0;
            int frag = 0;

            for(int i = 0; i < n.Length; i++)
            {
                int temp = n[i] -'0';
 
                if(k == 1)
                {
                    if(i == 0)
                        sum += temp;
                    else
                        sum += 9;
                }
                else if(k == 2)
                {
                    if(i == 0)
                        sum = (keta -1) * (temp -1) * 9;
                    else
                        sum += (keta -1) * 81;
 
                    if(temp != 0 && frag == 1)
                    {
                        sum += temp + (keta -1)* 9;
                        frag++;
                    }
                  
                  
                    if(i == 0)
                      frag++;
                        
 
                }
                else
                {
                    if(i == 0)
                        sum = (keta -1) * (keta -2) / 2 * (temp - 1) * 9 * 9;
                    else
                        sum += (keta -1) * (keta -2) / 2 * 9*9*9;
                    
                    if(temp != 0 && frag == 2)
                    {
                        sum += temp + (keta -1)*9;
                        frag++;
                    }
 
                    if(temp != 0 && frag == 1)
                    {
                        sum += (temp -1) * (keta -1) * 9+ (keta -1)*(keta -2) / 2 * 9*9;
                        frag++;
                    }
 
                    
                    
                    if(i == 0)
                        frag++;
                    
                    
                }
 
                keta--;
 
            }
            Console.WriteLine(sum);
            
        } 
    }