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;
#define rep(i,n) for(int i=0; i<(n); i++)
string s;
int k, ans, sz, t;
int main(){
	cin >> s >> k;
	sz = s.size();
	if(sz >= k) for(; k; k--){
		if(k == 3) ans += (sz - 1) * (sz - 2) * (sz - 3) / 6 * 9 * 9 * 9 + (s[t] - '1') * (sz - 1) * (sz - 2) / 2 * 9 * 9;
		else if(k == 2) ans += (sz - 1) * (sz - 2) / 2 * 9 * 9 + (s[t] - '1') * (sz - 1) * 9;
		else ans += (sz - 1) * 9 + (s[t] - '0');
		t++; sz--;
	}
	printf("%d\n",ans);
}