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)

d,m=1e9+7,l,dp[10001][2][100];S[9999];
char*s=S;
f(i,k,t,x,L)
{
	int*r=dp[i][t]+k;
	*r=i-l?*r:!k;
	if(!~*r)
	{
		*r=0;
		L=t?9:s[i]-48;
		for(x=0;x<=L;*r%=m)*r+=f(i+1,(k+x++)%d,t|x<L);
	}
	return*r;
}
main()
{
	scanf("%s%d",S,&d);
	memset(dp,-1,sizeof dp);
	l=strlen(s);
	printf("%d",(f(0,0,0)-1+m)%m);
}