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: Time Limit Exceeded)

d,m=1e9+7,dp[10001][2][100];
char s[11111];
dfs(i,k,t)
{
	if(i==strlen(s))return!k;
	int*r=dp[i][t]+k;
	if(~*r)return*r;
	*r=0;
	int L=t?9:s[i]-48;
	for(int l=0;l<=L;l++)
	{
		*r+=dfs(i+1,(k+l)%d,t|l<L);
		*r%=m;
	}
	return*r;
}
main()
{
	scanf("%s%d",s,&d);
	memset(dp,-1,sizeof dp);
	printf("%d",(dfs(0,0,0)-1+m)%m);
}