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 <vector>
#include <cmath>

using namespace std;

int combi(int n, int r) {
    int ans = 1;
    if (n < r) {
        return 0;
    }
    r = min(n - r, r);
    for (int i = 1; i <= r; i++) {
        ans = ans * (n - r + i) / i;
    }
    return ans;
}

int ctoi(char c) {
    return c - '0';
}

int count_zero(const string& s, int k) {
    int ans = 0;
    for (auto c: s) {
        if (c == '0') {
            ans++;
        }
    }
    return ans;
}

bool lower_bound(string& s, int k) {
    if (s.size() - k < 0) {
        s = "0";
        return false;
    }
    for (int i = int(s.size()-1); i > k; i--) {
        s[i] = '0';
    }
    return s.size() - count_zero(s, k) == k;
}

int main() {
    string n;
    int k;
    int ans = 0;
    cin >> n;
    cin >> k;
    if (!lower_bound(n, k)) {
        cout << 0 << endl;
        return 0;
    }
    for (int i = 0; i < n.size(); i++) {
        int a = ctoi(n[i]);
        if (a == 0) continue;
        if (k > 0) ans += combi(int(n.size() - (i + 1)), k) * int(pow(9, k));
        k--;
        ans += (a - 1) * combi(int(n.size() - (i + 1)), k) * int(pow(9, k));
    }
    ans += 1;
    cout << ans << endl;
    return 0;
}