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.Linq;

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

        int[,] mod = new int[13, 10];
        for (int i = 0; i < 13; i++)
            for (int j = 0; j < 10; j++)
                mod[i, j] = (10 * i + j) % 13;

        ulong[,] dp = new ulong[S.Length, 13];
        for (int i = 0; i < S.Length; i++)
        {
            if (i == 0)
            {
                if (S[0] == '?')
                    for (int j = 0; j < 10; j++)
                        dp[0, j] = 1;
                else
                    dp[0, S[0] - '0'] = 1;
            }
            else if (S[i] == '?')
            {
                for (int j = 0; j < 10; j++)
                    for (int k = 0; k < 13; k++)
                        dp[i, mod[k, j]] += dp[i - 1, k];
            }
            else
            {
                int j = S[i] - '0';
                for (int k = 0; k < 13; k++)
                    dp[i, mod[k, j]] += dp[i - 1, k];
            }
            for (int j = 0; j < 13; j++)
                dp[i, j] %= 1000000007;
        }

        Console.WriteLine(dp[dp.Length / 13 - 1, 5]);
    }
}