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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=205;
int p,n;
char s[N];
ll dp[N][4][2];
int main()
{
    scanf("%s",s+1);
    scanf("%d",&p);
    int n=strlen(s+1);
    dp[0][0][1]=1;
    for(int i=1;i<=n;i++)
        for(int j=0;j<=3;j++)
            for(int k=0;k<=1;k++)
        {
            int up=k?s[i]-'0':9;
            if(j==p) up=0;
            for(int h=0;h<=up;h++)
                dp[i][j+(h!=0)][k&&(h==up)]+=dp[i-1][j][k];
        }
    printf("%lld\n",dp[n][p][0]+dp[n][p][1]);
}