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: Time Limit Exceeded)

#include <stdio.h>
#pragma warning(disable : 4996)

long KNonZeroDigitedNumbers(N, K)
long K;
long N;
{
	long count = 0;
	for (long i = 0; i <= N; i++) {
		long nonZeroDigits = 0;
		long num = i;
		while (num != 0) {
			if (num % 10 != 0) {
				nonZeroDigits++;
			}
			num /= 10;
		}
		if (nonZeroDigits == K) {
			count++;
		}
	}
	return count;
}

main(void) {
	long N = 0;
	long K = 0;
	if (!scanf("%li", &N)) {
		printf("something wrong with input");
	}
	if (!scanf("%li", &K)) {
		printf("something wrong with input");
	}
	printf("%li\n", KNonZeroDigitedNumbers(N,K));
}