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 ABC135D
{
    class Program
    {
        static void Main(string[] args)
        {
            string S = Console.ReadLine();
            int L = S.Length;
            int mod = (int)Math.Pow(10, 9) + 7;
            long[,] dp = new long[L, 13];
            if (S[0].ToString() == "?")
            {
                for(int i = 0; i < 10; i++)
                {
                    dp[0, i] += 1;
                }
            }
            else
            {
                dp[0, int.Parse(S[0].ToString())] += 1;
            }
            for(int i = 1; i < L; i++)
            {
                if (S[i].ToString() == "?")
                {
                    dp[i, 0] += dp[i - 1, 0] + dp[i - 1, 1] + dp[i - 1, 2] + dp[i - 1, 3] + dp[i - 1, 5] + dp[i - 1, 6] + dp[i - 1, 7] + dp[i - 1, 9] + dp[i - 1, 10] + dp[i - 1, 11];
                    dp[i, 1] += dp[i - 1, 0] + dp[i - 1, 1] + dp[i - 1, 2] + dp[i - 1, 4] + dp[i - 1, 5] + dp[i - 1, 6] + dp[i - 1, 7] + dp[i - 1, 9] + dp[i - 1, 10] + dp[i - 1, 11];
                    dp[i, 2] += dp[i - 1, 0] + dp[i - 1, 1] + dp[i - 1, 2] + dp[i - 1, 4] + dp[i - 1, 5] + dp[i - 1, 6] + dp[i - 1, 8] + dp[i - 1, 9] + dp[i - 1, 10] + dp[i - 1, 11];
                    dp[i, 3] += dp[i - 1, 0] + dp[i - 1, 1] + dp[i - 1, 2] + dp[i - 1, 4] + dp[i - 1, 5] + dp[i - 1, 6] + dp[i - 1, 8] + dp[i - 1, 9] + dp[i - 1, 10] + dp[i - 1, 12];
                    dp[i, 4] += dp[i - 1, 0] + dp[i - 1, 1] + dp[i - 1, 3] + dp[i - 1, 4] + dp[i - 1, 5] + dp[i - 1, 6] + dp[i - 1, 8] + dp[i - 1, 9] + dp[i - 1, 10] + dp[i - 1, 12];
                    dp[i, 5] += dp[i - 1, 0] + dp[i - 1, 1] + dp[i - 1, 3] + dp[i - 1, 4] + dp[i - 1, 5] + dp[i - 1, 7] + dp[i - 1, 8] + dp[i - 1, 9] + dp[i - 1, 10] + dp[i - 1, 12];
                    dp[i, 6] += dp[i - 1, 0] + dp[i - 1, 1] + dp[i - 1, 3] + dp[i - 1, 4] + dp[i - 1, 5] + dp[i - 1, 7] + dp[i - 1, 8] + dp[i - 1, 9] + dp[i - 1, 11] + dp[i - 1, 12];
                    dp[i, 7] += dp[i - 1, 0] + dp[i - 1, 2] + dp[i - 1, 3] + dp[i - 1, 4] + dp[i - 1, 5] + dp[i - 1, 7] + dp[i - 1, 8] + dp[i - 1, 9] + dp[i - 1, 11] + dp[i - 1, 12];
                    dp[i, 8] += dp[i - 1, 0] + dp[i - 1, 2] + dp[i - 1, 3] + dp[i - 1, 4] + dp[i - 1, 6] + dp[i - 1, 7] + dp[i - 1, 8] + dp[i - 1, 9] + dp[i - 1, 11] + dp[i - 1, 12];
                    dp[i, 9] += dp[i - 1, 0] + dp[i - 1, 2] + dp[i - 1, 3] + dp[i - 1, 4] + dp[i - 1, 6] + dp[i - 1, 7] + dp[i - 1, 8] + dp[i - 1, 10] + dp[i - 1, 11] + dp[i - 1, 12];
                    dp[i, 10] += dp[i - 1, 1] + dp[i - 1, 2] + dp[i - 1, 3] + dp[i - 1, 4] + dp[i - 1, 6] + dp[i - 1, 7] + dp[i - 1, 8] + dp[i - 1, 10] + dp[i - 1, 11] + dp[i - 1, 12];
                    dp[i, 11] += dp[i - 1, 1] + dp[i - 1, 2] + dp[i - 1, 3] + dp[i - 1, 5] + dp[i - 1, 6] + dp[i - 1, 7] + dp[i - 1, 8] + dp[i - 1, 10] + dp[i - 1, 11] + dp[i - 1, 12];
                    dp[i, 12] += dp[i - 1, 1] + dp[i - 1, 2] + dp[i - 1, 3] + dp[i - 1, 5] + dp[i - 1, 6] + dp[i - 1, 7] + dp[i - 1, 9] + dp[i - 1, 10] + dp[i - 1, 11] + dp[i - 1, 12];
                    for(int j = 0; j < 13; j++)
                    {
                        dp[i, j] %= mod;
                    }
                }
                else
                {
                    for(int j = 0; j < 13; j++)
                    {
                        string s = j.ToString() + S[i].ToString();
                        int sint = int.Parse(s);
                        dp[i, sint % 13] += dp[i - 1, j];
                    }
                    for (int j = 0; j < 13; j++)
                    {
                        dp[i, j] %= mod;
                    }
                }
            }
            Console.WriteLine(dp[L - 1,5]);
        }
    }
}