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 <cstdlib>
#include <iostream>
#include <string>
#include <vector>
typedef long long LL;
constexpr int kMod = 1000000007;

LL dp[10000][101][2] = {};  // idx, sum%D, less/tight

int main() {
  std::string S; std::cin >> S;
  int D; std::cin >> D;

  dp[0][0][0] = 1;
  for (size_t idx = 0; idx < S.length(); ++idx) {
    int c = S[idx] - '0';
    for (int sum = 0; sum < D; ++sum) {
      for (int less : {0, 1}) {
        for (int n = 0; n < 10; ++n) {
          if (n<c)         dp[idx+1][(sum + n) % D][1] += dp[idx][sum][less];
          else if (n == c) dp[idx+1][(sum + n) % D][less] += dp[idx][sum][less];
          else if (less)   dp[idx+1][(sum + n) % D][less] += dp[idx][sum][less];

          dp[idx+1][(sum + n) % D][0] %= kMod;
          dp[idx+1][(sum + n) % D][1] %= kMod;
        }
      }
    }
  }

  std::cout << (dp[S.length()][0][0] + dp[S.length()][0][1] - 1) % kMod << std::endl;
}