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 <iostream>
#include <queue>
#include <utility>
#include <map>
#include <functional>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;

typedef long long ll;

const int mod = 1e9 + 7;
int md[100005], d, dp[10005][105][2];
string k;

void add2(int &a, int b)
{
    a = (a % mod + b % mod) % mod;
}

int f(int p, int m, int s)
{
    if (p == k.size() && m == 0)
        return 1;
    if (p == k.size())
        return 0;
    if (dp[p][m][s] != -1)
        return dp[p][m][s];
    int c = k[p] - '0', sm = 0;
    if (s)
        c = 9;
    for (int i = 0; i <= c; ++i)
        add2(sm, f(p + 1, (m + i) % d, (i != c) || s));
    return dp[p][m][s] = sm;
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cin >> k >> d;
    memset(dp, -1, sizeof dp);
    cout << f(0, 0, 0) - 1 << endl;
}