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)

import sys
input = sys.stdin.readline
K = list(map(int, list(input())[: -1]))
D = int(input())
mod = 10 ** 9 + 7
dp = [[0] * D for _ in range(len(K) + 1)]
dplim = [[0] * D for _ in range(len(K) + 1)]
dplim[0][0] = 1
for i in range(len(K)):
  for j in range(D):
    dplim[i + 1][(j + K[i]) % D] += dplim[i][j]
    for k in range(10):
      if k < K[i]:
        dp[i + 1][(j + k) % D] += dplim[i][j]
      dp[i + 1][(j + k) % D] += dp[i][j]
      dp[i + 1][(j + k) % D] %= mod
print(dp[-1][0] + dplim[-1][0] - 1)