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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

k = int(input())
d = int(input())

li = list(map(int,(list(str(k)))))
leng = len(li)
mod = 10**9+7

dp1 = [0 for _ in range(d)]
dp2 = [0 for _ in range(d)]

mm1 = li[0]
for i in range(mm1):
    dp2[i%d] = 1

for i in range(1,leng):
    for j in range(0,10):
        for l in range(d):
            #既にk以下であることが確定
            dp1[(l+j)%d] = (dp1[(l+j)%d]+dp2[l])%mod

        #上からi桁目でk以下が確定
        if j<li[i]:
            dp1[(mm1+j)%d] = (dp1[(mm1+j)%d]+1)%mod
    #print(dp1,dp2)
    

    mm1 = (mm1+li[i])%d
    dp2 = [dp1[i] for i in range(d)]
    dp1 = [0 for _ in range(d)]


print((dp2[0]-1)%mod)