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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder.Abc135
{
    class D
    {
        private static readonly long mod = 1000000007;

        public static void Main()
        {
            var s = Console.ReadLine();
            var n = s.Length;
            var dp = new long[n, 13];

            if (s[n - 1] == '?')
            {
                for (int i = 0; i <= 9; i++)
                    dp[0, i] = 1;
            }
            else
                dp[0, s[n - 1] - '0'] = 1;

            var d = 10;
            for (int i = 1; i < s.Length; i++)
            {
                if (s[n - 1 - i] == '?')
                {
                    for (int j = 0; j < 13; j++)
                    {
                        for (int k = 0; k <= 9; k++)
                        {
                            var r = (j + k * d) % 13;
                            dp[i, r] = (dp[i, r] + dp[i - 1, j]) % mod;
                        }
                    }
                }
                else
                {
                    int num = s[n - 1 - i] - '0';
                    for (int j = 0; j < 13; j++)
                    {
                        var r = (j + num * d) % 13;
                        dp[i, r] = dp[i - 1, j];
                    }
                }
                d = d * 10 % 13;
            }
            Console.WriteLine(dp[n - 1, 5]);
        }
    }
}