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 <cstring>
#define nmax 10005
using namespace std;
const int mod = 1e9 + 7;

int dp[nmax][2][105];
int n, d;
string s;

int  solve(int pos, int eq, int rest)
{
    if(pos == n) {
        if (rest == 0)
            return 1;
        return 0;
    }

    if(dp[pos][eq][rest] != -1)
        return dp[pos][eq][rest];

    int lim;
    long long tot = 0;

    if (eq)
        lim = s[pos] - '0';
    else
        lim = 9;

    for(int i = 0; i <= lim; i++)
        tot += solve(pos + 1, eq && (i == lim), (rest + i) % d );

    int itot = tot % mod;
    if (itot < 0)
        itot += mod;
    
    dp[pos][eq][rest] = itot;

    return itot;

}

int main()
{
    cin >> s;
    cin >> d;
    n = s.size();

    memset(dp,-1,sizeof(dp));

    int ans = solve(0,1,0) - 1;

    cout << ans << endl;

    return 0;

}