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 PyPy2 (5.6.0) (judge verdict: Runtime Error)

def f(i,s,e,d):
  if i==n:
    return s==0
  if (i,s,e) not in d:
    d[i,s,e]=sum(f(i+1,(s+j)%r,e and j==a[i]) for j in xrange(a[i]+1 if e else 10))%(pow(10,9)+7)
  return d[i,s,e]
a=map(int,list(raw_input().strip()))
n=len(a)
r=input()
print (f(0,0,True,{})-1)%(pow(10,9)+7)