D - Digits Parade

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 $10^9+7$.

??2??5

768

For example, $482305, 002865,$ and $972665$ satisfy the condition.

?44

1

Only $044$ satisfies the condition.

7?4

0

We may not be able to produce an integer satisfying the condition.

?6?42???8??2??06243????9??3???7258??5??7???????774????4?1??17???9?5?70???76???

153716888