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;

namespace atcoder135
{
    class Program
    {
        static void Main(string[] args)
        {
            string nm = Console.ReadLine();
            long[,] dp = new long[nm.Length + 1, 13];
            dp[0, 0] = 1;

            for (int i = 1; i <= nm.Length; ++i)
            {
                if (nm[i - 1] == '?')
                    for (int d = 0; d < 10; ++d)
                    {
                        for (int j = 0; j < 13; ++j)
                        {
                            int md = (j * 10 + d) % 13;
                            dp[i, md] = (dp[i, md] + dp[i - 1, j]) % ((int)1e9 + 7);
                        }
                    }
                else
                {
                    for (int j = 0; j < 13; ++j)
                    {
                        int md = (j * 10 + nm[i - 1] - '0') % 13;
                        dp[i, md] = (dp[i, md] + dp[i - 1, j]) % (int)(1e9 + 7);
                    }
                }
            }
            Console.WriteLine(dp[nm.Length, 5]);
        }
    }
}