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: Time Limit Exceeded)



MOD = 1000000007

def F(k, s):
    return dp[k][s]

def solve(n):
    resp = 0
    n = map(int, str(n))
    pref = 0
    for i in range(len(n)):
        for d in range(n[i]):
            resp += F(len(n) - i - 1, (pref - d) % D)
        pref -= n[i]
        pref %= D
    return resp


K = raw_input()
D = input()

# dp[i][j] = cant de numeros de i digitos con suma % d = j
dp = [[0] * D for _ in range(len(K) + 1)]
dp[0][0] = 1
for i in range(1, len(K) + 1):
    for j in range(D):
        for d in range(10):
            dp[i][j] += dp[i - 1][(j - d) % D]

resp = solve(K) - 1
if sum(map(int, str(K))) % D == 0:
    resp += 1
print(resp % MOD)