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 read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

trait ToU8 {
    fn to_u8(&self) -> Option<u8>;
}

impl ToU8 for char {
    fn to_u8(&self) -> Option<u8> {
        let num = (*self) as u8 - b'0';
        if num > 9u8 {
            None
        } else {
            Some(num)
        }
    }
}

const MOD: usize = 1_000_000_007;

fn main() {
    let s = read::<String>().chars().collect::<Vec<_>>();

    let mut dp = vec![vec![0; 13]; 100_005];

    dp[0][0] = 1;

    for (i, &c) in s.iter().enumerate() {
        
        for j in 0..10 {
            if let Some(c) = c.to_u8() {
                if c as usize != j {
                    continue;
                }
            }
            for ki in 0..13 {
                dp[i + 1][(ki * 10 + j) % 13] += dp[i][ki];
            }
        }

        for j in 0..13 {
            dp[i+1][j] %= MOD;
        }
    }

    let res = dp[s.len()][5];
    println!("{:?}", res);
}