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: Wrong Answer)

macro_rules! get {
    ($t:ty) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.trim().parse::<$t>().unwrap()
        }
    };
    ($($t:ty),*) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut iter = line.split_whitespace();
            (
                $(iter.next().unwrap().parse::<$t>().unwrap(),)*
            )
        }
    };
    ($t:ty; $n:expr) => {
        (0..$n).map(|_|
                    get!($t)
        ).collect::<Vec<_>>()
    };
    ($($t:ty),*; $n:expr) => {
        (0..$n).map(|_|
                    get!($($t),*)
        ).collect::<Vec<_>>()
    };
    ($t:ty |) => {
        {
            let mut line: String = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            line.split_whitespace()
                .map(|t| t.parse::<$t>().unwrap())
                .collect::<Vec<_>>()
        }
    };
    ($t:ty | $n:expr) => {
        (0..$n).map(|_| get!($t |)).collect::<Vec<_>>()
    };
}
macro_rules! tern {
    ($condition: expr, $_true: expr, $_false: expr) => {
        if $condition {
            $_true
        } else {
            $_false
        }
    };
}

fn main() {
    let S = get!(String).chars().rev().collect::<Vec<_>>();
    let L = S.len();

    let mut dp = vec![vec![0; 13]; L+1];
    let mod13 = [1, 10, 9, 12, 3, 4];
    dp[0][0] = 1;
    for i in 0..L {
        let mod13 = mod13[i % mod13.len()];
        for r in 0..13 {
            if S[i] == '?' {
                for n in 0..9 {
                    dp[i+1][(n * mod13 + r) % 13] += dp[i][r];
                    dp[i+1][(n * mod13 + r) % 13] %= 1_000_000_007;
                }
            } else {
                let n = (S[i] as u8 - '0' as u8) as usize;
                dp[i+1][(n * mod13 + r) % 13] += dp[i][r];
                dp[i+1][(n * mod13 + r) % 13] %= 1_000_000_007;
            }
        }
    }
    println!("{}", dp[S.len()][5]);
}