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: Accepted)

#include <bits/stdc++.h>

using namespace std;

const int M = 1e9 + 7;

void add_self(int& a, int b) {
    a += b;
    if (a >= M) {
        a -= M;
    }
}

int main(int argc, char *argv[])
{
    string K;
    int D;
    cin >> K >> D;
    int len = K.size();
    vector<vector<int>> dp(D, vector<int>(2));
    dp[0][0] = 1;
    for (int where = 0; where < len; where++) {
        auto dp_new = vector<vector<int>>(D, vector<int>(2));
        int limit = K[where] - '0';
        for (int sum = 0; sum < D; sum++) {
            for (int digit = 0; digit < limit; digit++) {
                add_self(dp_new[(sum + digit) % D][1], dp[sum][1] + dp[sum][0]);
            }
            add_self(dp_new[(sum + limit) % D][0], dp[sum][0]);
            add_self(dp_new[(sum + limit) % D][1], dp[sum][1]);
            for (int digit = limit + 1; digit <= 9; digit++) {
                add_self(dp_new[(sum + digit) % D][1], dp[sum][1]);
            }
        }
        dp = dp_new;
    }
    int res = dp[0][0];
    add_self(res, dp[0][1]);
    res -= 1;
    if (res < 0) res += M;
    cout << res << endl;
    return 0;
}