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<bits/stdc++.h>

using namespace std;

typedef long long ll;

const int N = 100005;
const int MOD = 1000000007;

vector<int> num;
int k; ll dp[N][105][2];

ll fun(int p, int s, int f) {
  if (p == num.size()) return s % k == 0;
  ll &ret = dp[p][s][f];
  if (ret != -1) return ret;
  ret = 0;
  int j = f ? 9 : num[p];
  for (int i = 0; i <= j; i++) {
    ret += fun(p + 1, (s + i) % k, i < j ? 1 : f);
    ret %= MOD;
  }
  return ret;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  string s;
  cin >> s >> k;
  for (auto i : s) {
    num.push_back(i - '0');
  }
  memset(dp, -1, sizeof dp);
  cout << fun(0, 0, 0) - 1 << endl;
  return 0;
}