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][200]={1};i,j,k,x,I;char s[11111];main(L){for(scanf("%s%d",s,&d);s[i];i+=j,j^=1)for(x=L=j?9:s[i]-48,k=0;~x;x-=++k/d,k%=d)p[i+1][I=(j|x<L)*d+(k+x)%d]+=p[i][j*d+k],p[i+1][I]%=m;printf("%d",(*p[i]+p[i][d]-1+m)%m);}