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)

/*https://bom.to/nxtvde2k1m4l*/
#include<bits/stdc++.h>
using namespace std;
template <typename A, typename B>
string to_string(pair<A, B> p);

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);

string to_string(const string& s) {
  return '"' + s + '"';
}

string to_string(const char* s) {
  return to_string((string) s);
}

string to_string(bool b) {
  return (b ? "true" : "false");
}

string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}

template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}

template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}

void debug_out() { cout << endl; }

template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cout << " " << to_string(H);
  debug_out(T...);
}

#define debug(...) cout << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define task "e"
typedef pair<int,int> ii;
typedef long long ll;
void init()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    freopen(task".inp","r",stdin);
    freopen(task".out","w",stdout);
}
int n;
ll dp[105][3][5];
string a;
ll cal(int pos, int ok, int j)
{
    if (j == 0) {
        return 1;
    }
    if (pos == n + 1) return 0;
    ll &res = dp[pos][ok][j];
    if (res != - 1) return res;
    res = 0;
    int low = 0, high = 9;
    if (ok) high = a[pos] - '0';
    for (int i = low; i <= high; i ++) {
        int new_ok = 0;
        if (ok && i == high) new_ok = 1;
        if (i == 0) res += cal(pos + 1, new_ok, j );
        else if (j - 1 >= 0) res += cal(pos+1,new_ok , j - 1);
    }
    return res;
}
int main()
{

    /// dp[i][j] the i_th digit and contains j
    cin >> a;
    int k ; cin >> k;
    a = " " + a;
    memset(dp,-1,sizeof(dp));
    n = a.length() - 1;
    cout << cal(1,0,k);
}