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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}
fn main() {
    let n: String = read();
    let mut dp = vec![vec![0; 13]; n.len() + 1];
    let big_int = 1000_000_000 + 7;
    dp[0][0] = 1; // pos, mod13

    for (i, c) in n.chars().enumerate() {
        if c == '?' {
            for j in 0..13 {
                for k in 0..10 {
                    let idx3: usize = (j * 10 + k) % 13;
                    dp[i + 1][idx3] += dp[i][j];
                    dp[i + 1][idx3] %= big_int;
                }
            }
        } else {
            for j in 0..13 {
                let idx3: usize = (j * 10 + c.to_digit(10).unwrap() as usize) % 13;
                dp[i + 1][idx3] += dp[i][j];
                dp[i + 1][idx3] %= big_int;
            }
        }
    }
    // debug!(dp);
    println!("{:?}", dp[n.len()][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()
}