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)

#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
template<class T> inline bool chmax(T& a,T b){if(a<b){a=b;return 1;} return 0;}
template<class T> inline bool chmin(T& a,T b){if(a>b){a=b;return 1;} return 0;}
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define all(vec) vec.begin(),vec.end()
typedef long long ll;
typedef pair<ll,ll> l_l;
typedef pair<int,int> i_i;
const ll mod=1e9+7;
const int inf=1<<30;

ll dp[110][4][2];

int main() {
  string s; cin >> s;
  int K; cin >> K;
  int n=s.size();
  dp[0][0][0]=1ll;
  rep(i,n)rep(j,K+1)rep(k,2){
    int nd=s[i]-'0';
    rep(d,10){
      int ni=i+1,nj=j,nk=k;
      if(d!=0) nj++;
      if(nj>K) continue;
      if(k==0){
        if(d>nd) continue;
        if(d<nd) nk=1;
      }
      dp[ni][nj][nk]+=dp[i][j][k];
    }
  }
  ll ans=dp[n][K][0]+dp[n][K][1];
  cout << ans << endl;
}