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)

def solve():
    MOD = 10**9 + 7

    strN = input().rstrip()
    D = int(input())

    maxD = len(strN)

    dp = [[[0]*(D) for j in range(2)] for i in range(maxD+1)]
    dp[0][0][0] = 1
    for d, Nd in enumerate(strN):
        Nd = int(Nd)
        for isLtN in range(2):
            for modD in range(D):
                dp[d][isLtN][modD] %= MOD
                for x in range(10):
                    if not isLtN and x > Nd: continue
                    isLtN2 = isLtN or x < Nd
                    modD2 = (modD+x) % D
                    dp[d+1][isLtN2][modD2] += dp[d][isLtN][modD]

    print((dp[-1][0][0] + dp[-1][1][0] - 1) % MOD)


solve()