Problem:
Score : 400 points

Problem Statement

Given is a string S. Each character in S is either a digit (0, ..., 9) or ?.

Among the integers obtained by replacing each occurrence of ? with a digit, how many have a remainder of 5 when divided by 13? An integer may begin with 0.

Since the answer can be enormous, print the count modulo 10^9+7.

Constraints

S is a string consisting of digits (0, ..., 9) and ?.

1 \leq |S| \leq 10^5

Input

Input is given from Standard Input in the following format:

S

Output

Print the number of integers satisfying the condition, modulo 10^9+7.

Sample Input 1

??2??5

Sample Output 1

768

For example, 482305, 002865, and 972665 satisfy the condition.

Sample Input 2

?44

Sample Output 2

1

Only 044 satisfies the condition.

Sample Input 3

7?4

Sample Output 3

0

We may not be able to produce an integer satisfying the condition.

Sample Input 4

?6?42???8??2??06243????9??3???7258??5??7???????774????4?1??17???9?5?70???76???

Sample Output 4

153716888

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

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

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ABC135.D();
        }
        class ABC135
        {
            public static void A()
            {
                var A = Read.Long();
                var B = Read.Long();
                Console.WriteLine(Math.Abs(A - B) % 2 == 0 ? ((A + B) / 2).ToString() : "IMPOSSIBLE");
            }
            public static void B()
            {
                var N = Read.Int();
                var P = Read.IntN();
                Console.WriteLine(P.Select((x, i) => x != i + 1).Count(x => x) <= 2 ? "YES" : "NO");
            }
            public static void C()
            {
                var N = Read.Int();
                var A = Read.LongN();
                var B = Read.LongN();
                long count = 0;
                for (int i = 0; i <= N; ++i)
                {
                    if (i > 0)
                    {
                        count += Math.Min(A[i], B[i - 1]);
                        A[i] = Math.Max(0, A[i] - B[i - 1]);
                    }
                    if (i < N)
                    {
                        count += Math.Min(A[i], B[i]);
                        B[i] = Math.Max(0, B[i] - A[i]);
                    }
                }
                Console.WriteLine(count);
            }
            public static void D()
            {
                var S = Read.Str();
                var N = S.Length;
                var P = 1000000007;
                var dp = new long[13, N + 1];
                dp[0, 0] = 1;
                for(int i = 0; i < N; ++i)
                {
                    var c = S[i];
                    if (c == '?')
                    {
                        for (int j = 0; j < 13; ++j)
                        {
                            for (int v = 0; v < 10; ++v)
                            {
                                dp[(j * 10 + v) % 13, i + 1] = (dp[(j * 10 + v) % 13, i + 1] + dp[j, i]) % P;
                            }
                        }
                    }
                    else
                    {
                        var v = c - '0';
                        for(int j = 0; j < 13; ++j)
                        {
                            dp[(j * 10 + v) % 13, i + 1] = dp[j, i];
                        }
                    }
                }
                Console.WriteLine(dp[5, N]);
            }
            public static void E()
            {

            }
            public static void F()
            {

            }
        }



        class Util
        {

        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN(); dict[ab[0]].Add(ab[1]);
                    if (!isDirectional) { dict[ab[1]].Add(ab[0]); }
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}