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;

namespace AtCoder.DP
{
    class EDPC_S
    {
        public const int mod = 1000000007;

        public static void Main()
        {
            var k = Console.ReadLine().Select(i => (byte)(i - '0')).ToArray();
            var d = int.Parse(Console.ReadLine());

            var dp = new long[k.Length + 1, d];


            var r = 0;
            for (int h = 0; h < k.Length; h++)
            {
                for (int i = 0; i < d; i++)
                {
                    for (int j = 0; j <= 9; j++)
                    {
                        int ij = (i + j) % d;
                        dp[h + 1, ij] = (dp[h + 1, ij] + dp[h, i]) % mod;
                    }
                }
                for (int j = 0; j < k[h]; j++)
                    dp[h + 1, (r + j) % d]++;
                r = (r + k[h]) % d;
            }

            var result = (dp[k.Length, 0] - 1 + (r == 0 ? 1 : 0)) % mod;
            Console.WriteLine(result);
        }
    }
}