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.Generic;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;

namespace AtCoder
{
	public class Program
	{
		static void Main(string[] args)
		{
			ulong MOD = 1000000007;

			string s = Console.ReadLine();
			int n = s.Length;

			ulong[,] dp = new ulong[100005, 13];
			dp[0, 0] = 1;

			for (int i = 0; i < n; i++) {
				for (int j = 0; j < 10; j++) {
					if (s[i] == '?' || s[i] == '0' + j) {
						for (int k = 0; k < 13; k++) {
							dp[i + 1, (k * 10 + j) % 13] += dp[i, k];
						}
					}
				}
				for (int k = 0; k < 13; k++) {
					dp[i + 1, k] %= MOD;
				}
			}
			Console.WriteLine(dp[n, 5]);
		}
	}
}