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.Collections.Generic;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {

            var s = Console.ReadLine().ToCharArray();
            var amaris = new int[6, 10]
            {
                { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 },
                { 0, 10, 7, 4, 1, 11, 8, 5, 2, 12 },
                { 0, 9, 5, 1, 10, 6, 2, 11, 7, 3 },
                { 0, 12, 11, 10, 9, 8, 7, 6, 5, 4 },
                { 0, 3, 6, 9, 12, 2, 5, 8, 11, 1 },
                { 0, 4, 8, 12, 3, 7, 11, 2, 6, 10 }
            };

            var amaripatternnum = new long[13];
            amaripatternnum[0] = 1;
            for (int i = s.Length - 1; i >= 0; i--)
            {
                int keta = s.Length - i - 1;
                if (s[i] == '?')
                {
                    var tempamaripatternnum = new long[13];
                    for (int n = 0; n < 10; n++)
                    {
                        int tempamari = amaris[keta % 6, n];
                        for (int j = 0; j < 13; j++)
                        {
                            tempamaripatternnum[(j + tempamari) % 13] += amaripatternnum[j];
                        }
                    }
                    for (int j = 0; j < 13; j++)
                    {
                        amaripatternnum[j] = tempamaripatternnum[j] % 1000000007;
                    }

                }
                else
                {
                    int n = int.Parse(s[i].ToString());
                    int tempamari = amaris[keta % 6, n];
                    var tempamaripatternnum = new long[13];
                    for (int j = 0; j < 13; j++)
                    {
                        tempamaripatternnum[(j + tempamari) % 13] = amaripatternnum[j];
                    }
                    amaripatternnum = tempamaripatternnum;
                }
            }
            Console.WriteLine(amaripatternnum[5]);


#if DEBUG
            Console.ReadKey();
#endif
        }
    }
}