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 Rust (1.15.1) (judge verdict: Accepted)

fn main() {
    let mo:u64 = 10u64.pow(9)+7;
    let s:Vec<char> = get_line().chars().collect();
    let mut p= vec![0u64;13]; p[0] = 1;
    for c in s.iter() {
        let mut v = vec![0u64;13];
        let candy = match c.to_digit(10) {
            Some(n) => {let u= n as usize; u..u+1} ,
            None => 0..10
        };
        for n in candy {
            for i in 0..13 {
                v[(i*10+n)%13] += p[i];
            }
        }
        p = v.iter().map(|e| e%mo).collect();
    }
    println!("{}",p[5]);
}

fn get_line() -> String {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).ok();
    buf.trim().to_owned()
}