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 <bits/stdc++.h>
using namespace std;
int main() {
    string s;
    cin >> s;
    long long n = s.length(), k;
    cin >> k;
    long long res = 0;
    if (k == 1) {
        if (n > 1) res = (n - 1) * 9;
        res += s[0] - '0';
    } else if (k == 2) {
        if (n > 2) res = (((n - 1) * (n - 2)) / 2) * 81;
        if (n > 1) {
            res += (s[0] - '0' - 1) * (n - 1) * 9;
            res += (s[1] - '0') + (n - 2) * 9;
        }
    } else {
        if (n > 3) res = (((n - 1) * (n - 2) * (n - 3)) / 6) * 729;
        if (n > 2) {
            res += (s[0] - '0' - 1) * (((n - 1) * (n - 2))/2) * 81;
            res += ((n - 2) * (n - 3) / 2) * 81;
            res += max(0, (s[1] - '0' - 1)) * (n - 2) * 9;
            res += (s[2] - '0') + (n - 3) * 9;
        }
    }
    cout << res;
    return 0;
}