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;

long long dp[10005][105];
int v[10005];
string s;
long long MOD = 1000000007;
int N, K;

int main(){
    cin >> s >> K;
    N = s.size();
    for(int i = 1; i<=N; i++){
        v[i] = s[N-i] - '0';
    }
    dp[0][0] = 1;
    for(int i = 1; i<=N; i++){
        for(int j = 0; j<K; j++){
            for(int d = 0; d<=9; d++){
                dp[i][(j+d)%K] += dp[i-1][j];
                dp[i][(j+d)%K] %= MOD;
            }
        }
    }
    int sum = 0;
    long long res = 0;
    for(int i = N; i>=1; i--){
        for(int j = 0; j < v[i]; j++){
            res += dp[i-1][((-(sum+j))%K + K)%K];
            res %= MOD;
        }
        sum += v[i];
    }
    if(sum%K){
        res = (res+MOD-1)%MOD;
    }
    cout << res << endl;
}