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 D___Digits_Parade
{
    class Program
    {
        static void Main(string[] args)
        {
            var S = Console.ReadLine();
            var N = new int[S.Length];
            for (int i = 0; i < S.Length; i++) N[i] = S[i] == '?' ? -1 : int.Parse(S[i].ToString());
            var MOD = 1000000007;
            var DP = new long[13, S.Length + 1];
            DP[0, 0] = 1;

            for (int i = 0; i < N.Length; i++)
            {
                for (int j = 0; j < 10; j++)
                {
                    if (N[i] != -1 && N[i] != j) continue;
                    for (int k = 0; k < 13; k++)
                    {
                        DP[(10 * k + j) % 13, i + 1] += DP[k, i];
                        DP[(10 * k + j) % 13, i + 1] %= MOD;
                    }
                }
            }
            Console.WriteLine(DP[5, S.Length]);
        }
    }
}