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 long MOD = 1000000007;

        static long Solve(string S)
        {
            S = string.Join("", S.Reverse());
            int N = S.Length;
            //dp[i, j] := i文字目までの値であまりがjとなるの通り
            long[,] dp = new long[N + 1, 13];
            //0文字目の時は値はないので余り0として1通りとする
            dp[0, 0] = 1;
            int ten = 1;

            //i文字目までの余りは dp[i - 1]
            //追加されるのは値S[i - 1] * 10^(i-1)
            //追加される余りはS[i - 1] * 10^(i-1) % 13 = add
            //i文字目までの全体の余りは add + dp[i - 1, j] (j = 0 ～ 12)
            for (int i = 1; i <= N; i++)
            {
                if (i == 1) ten = 1;
                else ten = (ten * 10) % 13;

                int val = -1;
                if (S[i - 1] != '?') val = S[i - 1] - '0';

                if(val != -1)
                {
                    for(int j = 0; j <= 12; j++)
                    {
                        dp[i, (((val * ten) % 13) + j) % 13] += dp[i - 1, j];
                    }                    
                }
                else
                {
                    //? = val = 0 ～ 9 において更新
                    for(val = 0; val <= 9; val++)
                    {
                        for (int j = 0; j <= 12; j++)
                        {
                            dp[i, ((val * ten) % 13 + j) % 13] += dp[i - 1, j];
                        }
                    }
                }

                for (int j = 0; j <= 12; j++) dp[i, j] %= MOD;

            }


            return dp[N, 5];
        }

        
        static void Main(string[] args)
        {
            //入力1(S)
            string S = Console.ReadLine();

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

}