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: Wrong Answer)

import sys
stdin = sys.stdin
 
sys.setrecursionlimit(10**5) 
 
def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x)-1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())

SIZE = 10**5+1
MOD = 10**9+7
k = ns().zfill(SIZE)
d = ni()

dp = [[[0]*(SIZE+1) for _ in range(d)] for _ in range(2)]

dp[1][0][0] = 1

for digit in range(SIZE):

    for num in range(10):
        if int(k[digit]) == num:
            for mod in range(d):
                dp[1][(mod+num)%d][digit+1] += dp[1][mod][digit]
                dp[1][(mod+num)%d][digit+1] %= MOD
        
        elif int(k[digit]) > num:
            for mod in range(d):
                dp[0][(mod+num)%d][digit+1] += dp[1][mod][digit]
                dp[0][(mod+num)%d][digit+1] %= MOD
        
        for mod in range(d):
            dp[0][(mod+num)%d][digit+1] += dp[0][mod][digit]
            dp[0][(mod+num)%d][digit+1] %= MOD

print(dp[0][0][-1] + dp[1][0][-1] - 1)