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: Time Limit Exceeded)

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

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var S = Read();
            var mod = (int)Math.Pow(10, 9) + 7;
            var pat = new long[S.Length + 1, 13];
            pat[0, 0] = 1;
            for (int i = 0; i < S.Length; i++)
            {
                if (S[i] == '?')
                {
                    for (int j = 0; j < 13; j++)
                    {
                        for (int k = 0; k < 10; k++)
                        {
                            if (pat[i, j] > 0)
                            {
                                var num = int.Parse(j.ToString() + k.ToString());
                                pat[i + 1, num % 13] += pat[i, j];
                                pat[i + 1, num % 13] %= mod;
                            }
                        }                        
                    }
                }
                else
                {
                    for (int j = 0; j < 13; j++)
                    {
                        if (pat[i, j] > 0)
                        {
                            var num = int.Parse(j.ToString() + S[i].ToString());
                            pat[i + 1, num % 13] += pat[i, j];
                            pat[i + 1, num % 13] %= mod;
                        }
                    }
                }
            }

            Console.WriteLine(pat[S.Length, 5]);
            Console.ReadLine();
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}