10734: ABC135 - D - Digits Parade
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Description
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 $10^9+7$.
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 $10^9+7$.
Input
Input is given from Standard Input in the following format:
```
$S$
```
```
$S$
```
Output
Print the number of integers satisfying the condition, modulo $10^9+7$.
Constraints
- $S$ is a string consisting of digits (`0`, ..., `9`) and `?`.
- $1 \leq |S| \leq 10^5$
- $1 \leq |S| \leq 10^5$
Sample 1 Input
??2??5
Sample 1 Output
768
For example, $482305, 002865,$ and $972665$ satisfy the condition.
Sample 2 Input
?44
Sample 2 Output
1
Only $044$ satisfies the condition.
Sample 3 Input
7?4
Sample 3 Output
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