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;
#define fr first
#define sc second
typedef long long ll ;
typedef double ld;
typedef pair<int,int> p2;
typedef pair<ll,p2> p3;
typedef vector<int> vi;
const ll  Mod = 7 + 1e9;
const ll  INF32 = 5 + 2e9;
const ll  INF64 = 5 + 1e18;
const ll  MAX = 5+ 1e4;

ll N,D,dp[MAX][105][2];
string K;

ll Try(int i,int sum,bool eq)
{
    if(i==N)
        return !sum;
    ll &r = dp[i][sum][eq];
    if( r != -1 )
        return r;
    r = 0;
    int cur = K[i] - '0';
    for(int j =(eq ? cur : 9); j>=0; j--)
        r = (r + Try(i+1,(sum + j)%D, eq && j == cur ))%Mod;
    return r;
}

int main()
{
    cin >> K >> D;
    N = K.size();
    memset(dp,-1,sizeof(dp));
    cout << Try(0,0,1)-1%Mod << endl;
    return 0;
}