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: Wrong Answer)

#include <iostream>
#include<cstdlib>
#include<queue>
#include<set>
#include<vector>
#include<string>
#include<cmath>
#include<algorithm>
#include<stack>
#include<map>
#include<deque>
#include<cstdio>
#include<cstdio>
#include<time.h>
using namespace std;
#define rep(i,a) for(int i=0;i<a;i++)
#define pd(a,n) for(int i=0;i<n;i++)cout<<a[i]<<((i==n-1)?"\n":" ")
#define pdd(a,n,m)for(int i=0;i<m;i++)pd(a,m)
#define mp make_pair
#define pb push_back
#define ll __int64
#define __int64 long long
#define P pair<int,int>
#define PP pair<P,int>

string s;
int k;
ll dp[1111][2][4];
ll N[1111];

int main(){
  cin>>s>>k;
  int n=s.size();
  rep(i,n)N[i]=s[i]-'0';
  dp[0][0][0]=1;
  rep(i,n){
    rep(f,2){
      rep(k,3){
        for(int x=0;x<=(f?9:N[i]);x++){
          dp[i+1][f||x<N[i]][k+(x!=0)]+=dp[i][f][k];
        }
      }
    }
  }
  cout<<dp[n][0][k]+dp[n][1][k]<<endl;

  return 0;
}