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;

class S
{
	static void Main()
	{
		var M = 1000000007;
		var k = Console.ReadLine();
		var d = int.Parse(Console.ReadLine());
		var n = k.Length;

		var dp = new long[n + 1, d, 2];
		dp[0, 0, 0] = 1;

		for (int i = 1; i <= n; i++)
		{
			var c = k[i - 1] - '0';

			for (int x = 0; x <= c; x++)
				for (int j = 0; j < d; j++)
					dp[i, (j + x) % d, x == c ? 0 : 1] += dp[i - 1, j, 0];
			for (int x = 0; x <= 9; x++)
				for (int j = 0; j < d; j++)
					dp[i, (j + x) % d, 1] += dp[i - 1, j, 1];

			for (int j = 0; j < d; j++)
			{
				dp[i, j, 0] %= M;
				dp[i, j, 1] %= M;
			}
		}
		Console.WriteLine((dp[n, 0, 0] + dp[n, 0, 1] + M - 1) % M);
	}
}