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;

/* macro */
#define rep(i,a,b) for(int i=a;i<b;i++)
#define revrep(i,a,b) for(int i = a; i > b; i--)
#define int long long
#define exist(s,e) ((s).find(e)!=(s).end())
#define all(v) (v).begin(), (v).end()
#define each(s,itr) for(auto (itr) = s.begin(); (itr) != s.end(); (itr)++)
#define sum(v) accumulate(all(v), (0LL))
#define pb push_back


/* alias */
template<class T> using vec = vector<T>;
typedef vector<int> vi;
typedef pair<int, int> pi;


/* constant */
const int inf = 1000100010010010;
const int mod = 1e9 + 7;
int dx[8]={1,0,-1,0,-1,1,-1,1};
int dy[8]={0,1,0,-1,-1,-1,1,1};


/* io_method */
int input(){int tmp;cin >> tmp;return tmp;}
string raw_input(){string tmp;cin >> tmp;return tmp;}
string readline(){string s;getline(cin, s);return s;}
template<class T> void printx(T n){cout << n;}
template<class T, class U> void printx(pair<T, U> p){cout << "(" << p.first << "," << p.second << ")";}
template<class T> void printx(vector<T> v){cout << "{";rep(i,0,v.size()){printx(v[i]);if(i != v.size()-1)printx(",");}cout << "}";}
template<class T> void print(T n){printx(n);cout << endl;}
template<class T> void print(set<T> s){cout << "{";each(s, e){if(e != s.begin()) printx(",");printx(*e);}cout << "}" << endl;}
template<class T, class U> void print(map<T, U> mp){cout << "{";each(mp, e){cout << "(" << e -> first << "," << e -> second << ")";}cout << "}" << endl;}


/* general_method */
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
//template<typename T> auto cut(T &a, int l, int r){return T(a.begin()+l, a.begin()+r);}

/* main */

string k;
int d;
int n;

int dp[10100][110][2];

int dfs(int i, int m, bool flag){

    if(i == n){
        if(m == 0) return 1;
        else return 0;
    }

    if(dp[i][m][flag] > -1) return dp[i][m][flag];

    int num = k[i] - '0';
    int ans = 0;
    rep(j,0,(flag ? num + 1 : 10)){
        ans += dfs(i + 1, (m + j) % d, (flag && j == num ? 1 : 0));
        ans %= mod;
    }

    return dp[i][m][flag] = ans;


}


signed main(){


    cin.tie(0);
    ios::sync_with_stdio(false);

    cin >> k >> d;
    n = k.size();
    memset(dp, -1, sizeof(dp));

    print(dfs(0, 0, 1) - 1);




    






    



    


    

}