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: Time Limit Exceeded)

import sys
sys.setrecursionlimit(100000)
n = int(input())
d = int(input())
p = 10**9+7
DP = {}
DP[-1] = [0]*d
DP[0] = [0]*d
DP[0][0] = 1
def dp(i):
    try:
        return DP[i]
    except:
        pass
    q, r = i//10, i % 10
    DP[i] = []
    for j in range(d):
        tmp = 0
        for k in range(r+1):
            tmp += dp(q)[(j-k) % d]
        for k in range(r+1, 10):
            tmp += dp(q-1)[(j-k) % d]
        DP[i].append(tmp % p)
    return DP[i]
print((dp(n)[0]-1) % p)