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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.math.BigInteger;
import java.util.*;

public class Main {

    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        String N = sc.next();
        int K = sc.nextInt();
        int res=0;
        for(int i=1;i<N.length();i++){
            StringBuilder bld = new StringBuilder();
            for(int k=0;k<i;k++){
                bld.append("9");
            }
            res += calc(bld.toString(), K);
        }
        res += calc(N, K);
        System.out.println(res);
    }

    public static int calc(String N, int K){
        int top = N.charAt(0)-'0';
        int L = N.length();
        if(L == 1){
            if(K==1){
                return top;
            }else{
                return 0;
            }
        }
        int nxt = N.charAt(1) - '0';
        int res = 0;
        if(K == 1){
            res = top + 9 * (L-1);
        }else if(K==2){
            if(L==1){return 0;}
            res = (top-1) * (L-1) * 9 + (L-2)*9+nxt;
        }else if(K==3){
            if(L <= 2){return 0;}
            res += com2(L-1) * 81 * (top-1);
            res += com2(L-2) * 81;
            res += (L - 2) * 9 * (nxt-1);
            res += (L - 3) * 9;
            res += (N.charAt(2) - '0');
        }
        return res;
    }

    public static int com2(int n){
        return n*(n-1)/2;
    }
}