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: Wrong Answer)

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

public class MainClass
{
	public const long Giri = 1000000007;
	
	public static void Main(string[] args)
	{
		var ki = Console.ReadLine();
		var d = Console.ReadLine().ToInt();
		
		var dp = new long[ki.Length+1, 2, d];	//i=何ケタ目, j=未満, k=あまり;
		dp[0,0,0] = 1;
		for(int i = 0; i < ki.Length; i++)
		{
			int keta = (int)(ki[i]-'0');
			for(int j = 0; j < 2; j++)
			{
				for(int k = 0; k < d; k++)
				{
					for(int l = 0; l <= (j == 0 ? keta : 9); l++)
					{
						dp[i+1, ((l < keta || j == 1) ? 1 : 0), ((k+l)%d)] += dp[i, j, k];
						dp[i+1, ((l < keta || j == 1) ? 1 : 0), ((k+l)%d)] %= Giri;
					}
				}
			}
		}
		Console.WriteLine((dp[ki.Length,1,0] + dp[ki.Length, 0, 0])%Giri-1);
	}
	
	static long GCD(long a, long b)
	{
		var v = new[] { a, b };
		while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
		return v[0];
	}
	public static string[] Input() { return Console.ReadLine().Split(' '); }
	public static int Clamp(int val, int max, int min = 0) { return Math.Min(max, Math.Max(min, val)); }
}

public static class Smarter
{
	public static int ToInt(this string str) { return int.Parse(str); }
	public static long ToLong(this string str) { return long.Parse(str); }
	public static int[] ToInt(this string[] str)
	{
		var r = new int[str.Length];
		for(int i = 0; i < str.Length; i++) r[i] = str[i].ToInt();
		return r;
	 }
}