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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#define mod 1000000007
#define Maxn 10005
#define Maxd 105
char s[Maxn];
int dp[Maxn][Maxd][2],p,d,len;
int dfs(int idx,int z,int t)
{
	if (idx==len) return !z;
	int *res=&dp[idx][z][t];
	if (~*res) return *res;*res=0;
	int x=s[idx]-'0',r=(t?x:9);
	for (int i=0;i<=r;i++)
		*res=(*res+dfs(idx+1,(z+i)%d,t&&i==r))%mod;
	return *res;
}
int main()
{
	memset(dp,-1,sizeof(dp));
	scanf("%s\n%d",s,&d);len=strlen(s);
	printf("%d\n",(dfs(0,0,1)-1+mod)%mod);
	return 0;
}