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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <string.h>
#include <unistd.h>
#include <stdlib.h>

#define lli long long int

int main(void)
{
	char input[102];
	char top[2];
	lli top_int;
	lli k;
	scanf("%s",input);
	scanf("%lld",&k);
	lli dig;
	lli out = 0;
	dig = strlen(input);
	top[0] = input[0];
	top[1] = '\0';
	top_int = strtol(top,NULL,10);
	if ( k == 1)
	{
		out = (dig-1) * 9 + 1;
		out = out + top_int - 1;
	}
	printf("%lld\n", out);
	return (0);
}