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<algorithm>
#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<map>
#include<cstdio>
#include<iomanip>
using namespace std;

int main()
{
    std::cout<<std::fixed<<std::setprecision(10);
    
    string N;
    int K;
    cin >> N >> K;
    vector<long long> dp = vector<long long>(4, 0);
    dp[0] = 1;
    int top = 0;
    
    for (int i = 0; i < N.size(); i++) {
        int x = N[i] - '0';
        for (int j = 3; j >= 1 ; j--) {
            if (top == j - 1) {
                dp[j] = (dp[j-1] - 1) * 9 + x;
            } else {
                dp[j] = dp[j-1] * 9 + dp[j];
            }
        }
        top++;
    }
    cout << dp[K];
    return 0;
}