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)

MOD = 10**9 + 7
K = input()
D = int(input())
N = len(K)
dp0 = [[0] * D for _ in range(N+1)]
dp1 = [[0] * D for _ in range(N+1)]
dp0[0][0] = 1
for i, digit in enumerate(K, 1):
    digit = int(digit)
    for d in range(D):
        for k in range(10):
            dp1[i][(d + k) % D] += dp1[i-1][d]
            dp1[i][(d + k) % D] %= MOD
            if k < digit:
                dp1[i][(d + k) % D] += dp0[i-1][d]
                dp1[i][(d + k) % D] %= MOD
            elif k == digit:
                dp0[i][(d + k) % D] += dp0[i-1][d]
                dp0[i][(d + k) % D] %= MOD
print((dp0[N][0] + dp1[N][0] - 1) % MOD)