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: Accepted)

k = input()
d = int(input())
mod = 10**9 + 7

dp = [[[0] * d for i in range(2)] for j in range(len(k)+1)]
dp[0][0][0] = 1

for i in range(len(k)):
    for j in range(2):
        for m in range(d):
            if j == 1:
                for num in range(10):
                    dp[i+1][j][(m+num)%d] += dp[i][j][m]
                    dp[i+1][j][(m+num)%d] %= mod
            else:
                for num in range(int(k[i])+1):
                    if num != int(k[i]):
                        dp[i+1][1][(m+num)%d] += dp[i][j][m]
                        dp[i+1][1][(m+num)%d] %= mod
                    else:
                        dp[i+1][0][(m+num)%d] += dp[i][j][m]
                        dp[i + 1][0][(m + num) % d] %= mod

print((dp[len(k)][0][0] + dp[len(k)][1][0] - 1) % mod)