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)

use std::io::Read;

pub fn read_stdin() -> String {
    let mut s = String::new();
    ::std::io::stdin().read_to_string(&mut s).unwrap();
    s
}

struct State {
    counts: [u64; 13],
    power: u64,
}

fn rec(st: State, c: char) -> State {
    let power = (st.power * 10) % 13;
    let range = if let Some(x) = c.to_digit(10) {
        x..(x + 1)
    } else {
        0..10
    };
    let mut counts = [0; 13];
    for i in range {
        let base = power * i as u64;
        for (j, &count) in st.counts.iter().enumerate() {
            let rem = ((base + j as u64) % 13) as usize;
            counts[rem] += count;
            counts[rem] %= 1_000_000_007;
        }
    }

    State {
        counts: counts,
        power: power,
    }
}

fn initialize(c: char) -> [u64; 13] {
    let mut a = [0; 13];
    if let Some(x) = c.to_digit(10) {
        a[x as usize] = 1;
    } else {
        for i in 0..10 {
            a[i] = 1;
        }
    }
    a
}

fn evaluate(v: Vec<char>) -> u64 {
    let init = State {
        counts: initialize(v[0]),
        power: 1,
    };
    v[1..].into_iter().fold(init, |st, &c| rec(st, c)).counts[5]
}

fn main() {
    let source = read_stdin();
    let mut iter = source.split_whitespace();
    let v: Vec<char> = iter.next().unwrap().chars().rev().collect();

    println!("{}", evaluate(v));
}