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: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
string s;
int ln,k;
ll fun(int id,int ch,int k)
{
	ll ans=0;
	int vl=s[id]-'0';
	if(k==0) return 1;
	if(k<0 || id>=ln) return 0;
	if(ch && !vl) ans=fun(id+1,1,k);
	else ans=fun(id+1,0,k);
	for(int i=1;i<=9;i++)
	{
		if(ch)
		{
			if(i<vl) ans+=fun(id+1,0,k-1);
			else if(i==vl) ans+=fun(id+1,1,k-1);
		}
		else ans+=fun(id+1,0,k-1);
	}
	return ans;
}
int main()
{
	cin>>s>>k;
	ln=s.length();
	cout<<fun(0,1,k);
	return 0;
}