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;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

ll dp[101010][111][2];

int main(){
  string K; cin>>K;
  int D; cin>>D;
  reverse(K.begin(),K.end());
  dp[K.length()][0][0]=1;
  for(int i=K.length()-1;i>=0;i--) rep(j,D){
    int num=K[i]-'0';
    rep(k,10){
      (dp[i][(j+k)%D][1]+=dp[i+1][j][1])%=MOD;
      if(k<num) (dp[i][(j+k)%D][1]+=dp[i+1][j][0])%=MOD;
      if(k==num) (dp[i][(j+k)%D][0]+=dp[i+1][j][0])%=MOD;
    }
  }
  cout<<(dp[0][0][0]+dp[0][0][1])%MOD-1<<endl;
  return 0;
}