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;
using System.Linq;

namespace CSharpSample01
{


    class Program
    {

        const int MOD = 1000000007;

        static long Solve(string S)
        {
            int n = S.Length;

            S = string.Join("", S.Reverse());
            
            long[,] dp = new long[n + 1, 13];

            dp[0, 0] = 1;

            for(int j = 1; j < 13; j++)
            {
                dp[0, j] = 0;
            }
            
            int ten = 0;

            for(int i = 0; i < n; i++)
            {
                if (i == 0) ten = 1;
                else ten = (ten * 10) % 13;
                

                int c;
                if (S[i] == '?') c = -1;
                else c = S[i] - '0';

                for (int j = 0; j < 13; j++)
                {
                    for(int k = 0; k <= 9; k++)
                    {
                        if(c != -1)
                        {
                            dp[i + 1, (c * ten + j) % 13] += dp[i, j];
                            break;
                        }
                        dp[i + 1, (k * ten + j) % 13] += dp[i, j];
                    }       
                    
                }  
                
                for(int j = 0; j < 13; j++)
                {
                    dp[i + 1, j] %= MOD;
                }

            }

            
            return dp[n, 5];
        }

        
        static void Main(string[] args)
        {
            string S = Console.ReadLine();

            
            Console.WriteLine(Solve(S));
        }
    }
}