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 (7.3.0) (judge verdict: Wrong Answer)

d = int(input())
n = input()
t = len(n)
mod = 10**9 + 7
dp1 = [[0 for i in range(d)] for j in range(t)]
dp2 = [[0 for i in range(d)] for j in range(t)]

dp1[0][int(n[0])%d] += 1
for i in range(int(n[0])):
    dp2[0][i%d] += 1
    
for i in range(1,t):
    now = int(n[i])
    for j in range(10):
        if j == now:
            for k in range(d):
                dp1[i][(k+j)%d] += dp1[i-1][k]
                dp2[i][(k+j)%d] += dp2[i-1][k]
                dp1[i][(k+j)%d] %= mod
                dp2[i][(k+j)%d] %= mod
        elif j < now:
            for k in range(d):
                dp2[i][(k+j)%d] += dp1[i-1][k]
                dp2[i][(k+j)%d] += dp2[i-1][k]
                dp2[i][(k+j)%d] %= mod
        else:
            for k in range(d):
                dp2[i][(k+j)%d] += dp2[i-1][k]
                dp2[i][(k+j)%d] %= mod

print((dp1[-1][0]+dp2[-1][0]-1)%mod)