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 Ruby (2.3.3) (judge verdict: Wrong Answer)

s,d=*$<;
d=d.to_i;
m=10**9+7;
p=[0]*d*2;
p[0]=1;
s.chop.bytes{|b|
	q=[0]*d*2;
	2.times{|j|
		u=[b-48,9][j];
		(0..u).each{|l|
			d.times{|k|
				q[(j>0||l<u ? d : 0)+(k+l)%d]+=p[j*d+k];
			}
		}
	}
	p=q.map{|q|q%m}
}
p (p[0]+p[d]-1)%m