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.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
using static AtCoder.Tool;
namespace AtCoder
{
    class AC
    {
        const int MOD = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;
        const double EPS = 1e-8;
        static readonly int[] dx = { 0, 1, 0, -1 };
        static readonly int[] dy = { 1, 0, -1, 0 };
        static List<List<int>> G = new List<List<int>>();
        //static List<List<Edge>>G = new List<List<Edge>>();
        //static List<Edge> E = new List<Edge>();
        
        
        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            string K = Console.ReadLine();
            int D = int.Parse(Console.ReadLine());

            int L = K.Length;
            var dp = new long[L + 1, D, 2];

            for(var i = 0; i <= L; i++)
            {
                for(var j = 0; j < D; j++)
                {
                    dp[i, j, 0] = 0;
                    dp[i, j, 1] = 0;
                }
            }

            dp[0, 0, 0] = 1;
            for(var i = 0; i < L; i++)
            {
                int nx = K[i] - '0';
                for(var r = 0; r < D; r++)
                {
                    dp[i + 1, (r + nx) % D, 0] += dp[i, r, 0];
                    dp[i + 1, (r + nx) % D, 0] %= MOD;

                    for (var k = 0; k < nx; k++)
                    {
                        dp[i + 1, (r + k) % D, 1] += dp[i, r, 0];
                        dp[i + 1, (r + k) % D, 1] %= MOD;
                    }

                    for(var k = 0; k < 10; k++)
                    {
                        dp[i + 1, (r + k) % D, 1] += dp[i, r, 1];
                        dp[i + 1, (r + k) % D, 1] %= MOD;
                    }
                }
            }
            
            Console.WriteLine((dp[L, 0, 0] + dp[L, 0, 1] - 1 + MOD) % MOD);

            //Console.Out.Flush();
        }

        
        struct Edge
        {
            public int from;

            public int to;
            public long dist;
            public Edge(int t, long c)
            {
                from = -1;
                to = t;
                dist = c;
            }
            public Edge(int f, int t, long c)
            {
                from = f;
                to = t;
                dist = c;
            }

        }
        struct Pair<T, U> : IComparable<Pair<T, U>>
        where T : IComparable<T>
        where U : IComparable<U>
        {
            public T first;
            public U second;
            private readonly bool CompWithFirst;

            public Pair(T f, U s, int comp)
            {
                first = f;
                second = s;
                CompWithFirst = comp == 1;
            }
            public Pair(T f, U s)
            {
                first = f;
                second = s;
                CompWithFirst = true;
            }

            public int CompareTo(Pair<T, U> other)
            {
                return CompWithFirst ? first.CompareTo(other.first) : second.CompareTo(other.second);
            }
        }
    }
    public class UnionFind
    {
        public int[] parent;
        public int[] rank;
        public int[] size;
        public UnionFind(int n)
        {
            parent = new int[n];
            rank = new int[n];
            size = new int[n];
            for (var i = 0; i < n; i++)
            {
                parent[i] = i;
                rank[i] = 0;
                size[i] = 1;
            }
        }

        private int Root(int x)
        {
            return parent[x] == x ? x : parent[x] = Root(parent[x]);
        }

        public bool SameRoot(int x, int y)
        {
            return Root(x) == Root(y);
        }

        public void Unite(int x, int y)
        {
            x = Root(x);
            y = Root(y);
            if (x == y) { return; }

            if (rank[x] < rank[y])
            {
                parent[x] = y;
                size[y] += size[x];
                size[x] = 0;
            }
            else
            {
                parent[y] = x;
                if (rank[x] == rank[y]) { rank[x]++; }
                size[x] += size[y];
                size[y] = 0;
            }
        }

        public int SizeOf(int x)
        {
            return size[Root(x)];
        }

    }
    public class PriorityQueue<T> where T : IComparable<T>
    {

        private List<T> Q;
        private readonly int r;

        public PriorityQueue(bool ascending)
        {
            if (ascending)
            {
                r = 1;
            }
            else
            {
                r = -1;
            }
            Q = new List<T>();
        }


        private void PushHeap(List<T> list, T item)
        {
            int n = list.Count();
            list.Add(item);

            while (n != 0)
            {
                int pIndex = (n - 1) / 2;

                if (list[n].CompareTo(list[pIndex]) * r > 0)
                {
                    Swap(Q, n, pIndex);
                }
                else { break; }

                n = pIndex;
            }
        }

        private void PopHeap(List<T> list)
        {
            int n = list.Count() - 1;
            list[0] = list[n];
            list.RemoveAt(n);

            int cur = 0;
            int comp;

            while (2 * cur + 1 <= n - 1)
            {
                int c1 = 2 * cur + 1;
                int c2 = 2 * (cur + 1);
                if (c1 == n - 1)
                {
                    comp = c1;
                }
                else
                {

                    comp = list[c1].CompareTo(list[c2]) * r > 0 ? c1 : c2;
                }

                if (list[cur].CompareTo(list[comp]) * r < 0)
                {
                    Swap(Q, cur, comp);
                }
                else { break; }

                cur = comp;
            }
        }

        private void Swap(List<T> list, int a, int b)
        {
            T keep = list[a];
            list[a] = list[b];
            list[b] = keep;
        }



        public void Enqueue(T value)
        {
            PushHeap(Q, value);
        }

        public T Dequeue()
        {
            T ret = Q[0];
            PopHeap(Q);
            return ret;
        }

        public T Peek()
        {
            return Q[0];
        }

        public int Count()
        {
            return Q.Count();
        }

        public bool Contains(T search)
        {
            return Q.Contains(search);
        }
    }
    public class Scanner
    {
        public int[] SplitRead()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReadL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }
    public static class Tool
    {
        static public void Initialize<T>(ref T[] array, T initialvalue)
        {
            for (var i = 0; i < array.Length; i++)
            {
                array[i] = initialvalue;
            }
        }
        static public void Swap<T>(T[] a, int i, int j)
        {
            T k = a[i];
            a[i] = a[j];
            a[j] = k;
        }

        static public void Display<T>(T[,] array2d, int n, int m)
        {
            for(var i = 0; i < n; i++)
            {
                for(var j = 0; j < m; j++)
                {
                    Console.Write($"{array2d[i, j]} ");
                }
                Console.WriteLine();
            }
        }

    }

}