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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <cstdio>
#include <cstring>

const int MAXN = 1e4+4;
const int MAXD = 1e2+2;
const int MOD = 1e9+7;


int mem[MAXN][MAXD][2];
bool solved[MAXN][MAXD][2];
char C[MAXN];
int d, n;

int dp(int x, int sum, bool less) {
  if (x == n) return sum == 0;
  int &ret = mem[x][sum][less];
  if (solved[x][sum][less]) return ret;
  solved[x][sum][less] = 1;
  
  int k = less == 0 ? C[x] - '0' : 9;
  for (int i = 0; i <= k; ++i) {
    ret = (ret + dp(x+1, (sum+i) % d, less | (i < (C[x] - '0')))) % MOD;
  }

  return ret;
}

int main() {
  scanf("%s%d", C, &d);
  n = strlen(C);
  printf("%d\n", dp(0, 0, 0)-1);
  return 0;
}