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.Collections;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class D
{
	public static void Main()
	{
		long mod = (long)(1e9 + 7);
		string S = GetString();
		int N = S.Length;
		long[,] dp = new long[N, 13];
		if(S[0] == '?')
		{
			for(int i = 0; i < 10; i++)
				dp[0, i] = 1;
		}
		else
		{
			dp[0, (int)(S[0] - '0')] = 1;
		}

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

		Console.WriteLine(dp[N - 1, 5]);
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}