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 PyPy2 (5.6.0) (judge verdict: Accepted)

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

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

for i in range(L):
    nd = int(K[i])
    for j in range(D):
        for k in range(2):
            #lim = 9 if k == 1 else nd
            for d in range(10):
                nk = k
                if k == 0:
                    if d > nd:
                        continue
                    if d < nd:
                        nk = 1
                dp[i+1][(j+d) % D][nk] += dp[i][j][k]
                dp[i+1][(j+d) % D][nk] %= mod

ans = (dp[L][0][0]+dp[L][0][1]-1+mod) % mod

#for i in range(L+1):
#    print(dp[i])
print(ans)