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

class Solve
{
	const int mod = 1000000007;
	static void Main(string[] args)
	{
		string s = Console.ReadLine();
		int N = s.Length;
		long[,] dp = new long[N+1, 13];
		dp[0, 0] = 1;

        for(int i = 0; i < N; i++)
		{
			if (s[i] != '?')
			{
				int sint = s[i] - '0';
                for(int j = 0; j < 13; j++)
				{
					dp[i + 1, (10 * j + sint) % 13] = dp[i, j] % mod;
				}
			}
			else
			{
                for(int j = 0; j <=9; j++)
				{
                    for(int k = 0; k < 13; k++)
					{
						dp[i + 1, (10 * k + j) % 13] += dp[i, k];
						dp[i + 1, (10 * k + j) % 13] %= mod;
					}
				}
			}
		}
		Console.WriteLine(dp[N, 5]);

	}
}