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: Runtime Error)

import sys
sys.setrecursionlimit(10**8)

M = 10**9 + 7
K = int(input())
D = int(input())

dp = [[None] * 100 for _ in range(10**5 + 1)]
def f(k, i):
    if dp[i][k] is not None:
        return dp[i][k]

    if i == 0:
        r = (k % D) == 0
        dp[i][k] = r
        return r
    r = sum(f((k + x) % D, i - 1) for x in range(0, 10)) % M
    dp[i][k] = r
    return r

sk = str(K)
dig = len(sk)
answer = 0
s = sum(map(int, list(sk)))
for j in range(int(sk[-1]) + 1):
    if (s - j) % D == 0:
        answer += 1

if dig > 1:
    s -= int(sk[-1])
    for i in range(dig - 1, 1, -1):
        if sk[i - 1] == "0":
            continue
        for j in range(int(sk[i - 1])):
            answer += f(s - 1 - j, dig - i)
        s -= int(sk[i - 1])

    for k in range(1, int(sk[0])):
        answer += f(k, dig - 1)

    if dig > 1: # 先頭0固定
        for k in range(10):
            answer += f(k, dig - 2)


print((answer - 1) % M)