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)

const MOD: i32 = 1000000000 + 7;

fn main() {
    let mut s: Vec<char> = read::<String>().chars().collect();
    let len = s.len();
    s.reverse();
    let mut dp = vec![vec![0i32; 13]; len];
    match s[0] {
        '?' => {
            for i in 0..10 {
                dp[0][i] = 1;
            }
        },
        c => dp[0][c as usize - 48] = 1,
    }
    for i in 1..len {
        let mul = 10usize.pow((i % 13) as u32) % 13;
        match s[i] {
            '?' => {
                for m in 0..10 {
                    for n in 0..13 {
                        let new_r = (m * mul + n) % 13;
                        dp[i][new_r] += dp[i - 1][n];
                        dp[i][new_r] %= MOD;
                    }
                }
            },
            c => {
                let num = c as usize - 48;
                for n in 0..13 {
                    let new_r = (num * mul + n) % 13;
                    dp[i][new_r] += dp[i - 1][n];
                    dp[i][new_r] %= MOD;
                }
            },
        }
    }
    println!("{}", dp[len - 1][5]);
}

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()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}