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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

char s[111111];

int m=1e9+7,dp[10009][2][100],p,d;


int dfs(int idx,int z,bool tight){
  if(idx==strlen(s))return !z;
  int &res=dp[idx][tight][z];
  if(~res)return res;
  res=0;
  int r=(tight?9:s[idx]-48);
  for(int i=0;i<=r;i++){
    res+=dfs(idx+1,(z+i)%d,tight||i<r);
    res%=m;
  }
  return res;
}

int main(){
  memset(dp,-1,sizeof dp);
  scanf("%s%d",s,&d);
  cout<<(dfs(0,0,0)-1+m)%m<<endl;
}
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