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