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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

public static class Program {
    static int mod=1000000007;
    public static void Main() {
        String s=Console.ReadLine();
        int n=s.Length;
        int[]a=new int[n];
        for(int i=0;i<n;i++){
            a[i]=s[i]-'0';
        }
        int d=int.Parse(Console.ReadLine());
        int[,]dp=new int[d,2];
        dp[0,0]=1;
        for(int i=0;i<n;i++){
            int[,]swp=new int[d,2];
            for(int j=0;j<d;j++){
                Add(ref swp[(j+a[i])%d,0], dp[j,0]);
                for(int k=0;k<a[i];k++){
                    Add(ref swp[(j+k)%d,1],dp[j,0]);
                }
                for(int k=0;k<10;k++){
                    Add(ref swp[(j+k)%d,1], dp[j,1]);
                }
            }
            dp=swp;
        }
        Console.WriteLine((dp[0,0]+dp[0,1]+mod-1)%mod);
    }
    public static void Add(ref int x, int y){
        x+=y;
        if(mod<=x)x-=mod;
    }
}