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: Runtime Error)

#include<bits/stdc++.h>
#define mp make_pair
#define fi first
#define se second
#define VAL 100000
#define ll long long
#define INF 10000000000000000LL
#define pll pair<long long , long long>
const int MAX=1e4+10;
const ll MOD=1e9+7;
const int TOT_PRIMES=19;
const int MAX_A=70;
using namespace std;
int D;
ll dp[MAX][300][3];
int n;
string K;
bool vis[MAX][300][3];
ll solve(int idx, int cur , bool f){
	if(idx==n){
//		if(cur%D==0)
//			cout<<cur<<" "<<idx<<"\n";
		return cur%D==0;
	}
	
	if(vis[idx][cur][f])
		return dp[idx][cur][f];
	vis[idx][cur][f]=true;
	int lmt=9;
	if(f){
		lmt=K[idx]-'0';
	}
	ll ans=0;
	for(int i=0;i<=lmt;i++){
		int p=cur+i;
		p=p%D;
		ans=(ans + solve(idx+1, p, f&&(i==K[idx]-'0')))%MOD;
		ans=ans%MOD;
	}
	return dp[idx][cur][f]=ans%MOD;
}
int main() 
{ 
	//ios_base::sync_with_stdio(false);
  //  cin.tie(NULL);	
	#ifndef ONLINE_JUDGE
	freopen("inp.txt" ,"r", stdin );
	freopen("out.txt", "w", stdout);
	#endif
	cin>>K;
	cin>>D;
	n=K.size();
	ll ans=solve(0 , 0 ,true);
	cout<<(ans-1)%MOD<<"\n";
	
}