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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

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

length = len(K)
dp = [[[0] * D for _ in range(2)] for _ in range(length + 1)]
dp[0][0][0] = 1

for i in range(length):
    for j in range(2):
        for k in range(D):
            if j == 1:
                x = 9
            else:
                x = int(K[i])
            for d in range(x + 1):
                dp[i + 1][j or d < x][(k + d) % D] += dp[i][j][k]
                dp[i + 1][j or d < x][(k + d) % D] %= mod
ans = 0
for i in range(2):
    ans += dp[length][i][0]

print((ans - 1) % mod)