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>
#define F first
#define S second
#define ll long long
#define pb push_back

using namespace std;

const ll N=1e4+5;

ll mod=1e9+7;
ll mem[N][105][2],n;
int d;

string k;

ll dp(int pos,int m,bool flag)
{
    if (pos==n)
    {
        return (m==0);
    }
    if (mem[pos][m][flag]!=-1)return mem[pos][m][flag];
    ll ans=0;
    for (int i=0;i<=(flag?9:(k[pos]-'0'));i++)
    {
        ans+=dp(pos+1,(m+i)%d,flag|i<(k[pos]-'0'));
        ans%=mod;
    }
    ans%=mod;
    return mem[pos][m][flag]=ans;
}

int main()
{
    memset(mem,-1,sizeof mem);
    cin >> k >> d;
    n=k.length();
    cout << dp(0,0,0)-1 << endl;
    return 0;
}