Problem:
Score : 100 points

Problem Statement

Find the number of integers between 1 and K (inclusive) satisfying the following condition, modulo 10^9 + 7:

The sum of the digits in base ten is a multiple of D.

Constraints

All values in input are integers.

1 \leq K < 10^{10000}

1 \leq D \leq 100

Input

Input is given from Standard Input in the following format:

K
D

Output

Print the number of integers satisfying the condition, modulo 10^9 + 7.

Sample Input 1

30
4

Sample Output 1

6

Those six integers are: 4, 8, 13, 17, 22 and 26.

Sample Input 2

1000000009
1

Sample Output 2

2

Be sure to print the number modulo 10^9 + 7.

Sample Input 3

98765432109876543210
58

Sample Output 3

635270834

Solution in C (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>

const int Mod = 1000000007;

int main()
{
	int D;
	char K[10001];
	scanf("%s", K);
	scanf("%d", &D);
	
	int i, j, k, tmp = 0;
	long long dp[2][101] = {};
	for (i = 0; K[i] != 0; i++) {
		for (j = 0; j < D; j++) dp[i%2][j] = 0;
		for (j = 0; j < D; j++) {
			for (k = 0; k <= 9; k++) dp[i%2][(j+k)%D] += dp[1-i%2][j];
		}
		for (k = 0; k < K[i] - '0'; k++) dp[i%2][(tmp+k)%D]++;
		tmp = (tmp + K[i] - '0') % D;
		for (j = 0; j < D; j++) dp[i%2][j] %= Mod;
	}
	if (tmp == 0) printf("%lld\n", dp[1-i%2][0]);
	else printf("%lld\n", (dp[1-i%2][0] - 1 + Mod) % Mod);
	fflush(stdout);
	return 0;
}