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)

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::fs::File;
#[allow(unused_imports)]
use std::io::prelude::*;
#[allow(unused_imports)]
use std::io::Stdin;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufReader, BufWriter, Write};
#[allow(unused_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::str::FromStr;

type BoxResult<T> = Result<T, Box<std::error::Error>>;

const MOD: usize = 1_000_000_000 + 7;

fn main() {
    let mut scanner = Scanner::new(stdin());
    let mut digits = scanner.read_chars().unwrap();
    let mut carried = false;
    for i in (0..digits.len()).rev() {
        if digits[i].is_digit(10) {
            let digit = digits[i].to_digit(10).unwrap();
            if i == digits.len() - 1 {
                if digit >= 5 {
                    digits[i] = std::char::from_digit(digit - 5, 10).unwrap();
                    break;
                } else {
                    carried = true;
                    digits[i] = std::char::from_digit(10 + digit - 5, 10).unwrap();
                }
            } else {
                if digit >= 1 {
                    carried = false;
                    digits[i] = std::char::from_digit(digit - 1, 10).unwrap();
                    break;
                } else {
                    digits[i] = '9';
                }
            }
        } else {
            break;
        }
    }
    if carried {
        println!("0");
        return;
    }
    let mut dp = vec![0; 13];
    dp[0] = 1;
    for i in (0..digits.len()).rev() {
        let mut dp_new = vec![0; 14];
        if digits[i].is_digit(10) {
            let digit = digits[i].to_digit(10).unwrap() as usize;
            for j in 0..13 {
                for k in 0..10 {
                    let num = 13 * k + j;
                    let d = num % 10;
                    let index = num / 10;
                    if d != digit {
                        continue;
                    }
                    dp_new[index] = (dp_new[index] + dp[j]) % MOD;
                }
            }
        } else {
            for j in 0..13 {
                for k in 0..10 {
                    let num = 13 * k + j;
                    let index = num / 10;
                    dp_new[index] = (dp_new[index] + dp[j]) % MOD;
                }
            }
        }
        dp = dp_new;
    }
    println!("{}", dp[0]);
}

#[allow(dead_code)]
struct Scanner<R> {
    reader: BufReader<R>,
    buffer: String,
}

impl<R> Scanner<R>
where
    R: Read,
{
    #[allow(dead_code)]
    fn new(inner: R) -> Scanner<R> {
        let reader = BufReader::new(inner);
        let buffer = String::new();
        Scanner { reader: reader, buffer: buffer }
    }

    #[allow(dead_code)]
    fn with_capacity(capacity: usize, inner: R) -> Scanner<R> {
        let reader = BufReader::with_capacity(capacity, inner);
        let buffer = String::new();
        Scanner { reader: reader, buffer: buffer }
    }

    #[allow(dead_code)]
    fn read<T>(&mut self) -> BoxResult<T>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed = self.buffer.trim().parse()?;
        self.buffer.clear();
        Ok(parsed)
    }

    #[allow(dead_code)]
    fn read_vector<T>(&mut self) -> BoxResult<Vec<T>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed_vec = self
            .buffer
            .trim()
            .split_whitespace()
            .map(|s| s.parse())
            .collect::<Result<Vec<_>, _>>()?;
        self.buffer.clear();
        Ok(parsed_vec)
    }

    #[allow(dead_code)]
    fn read_matrix<T>(&mut self, lines: usize) -> BoxResult<Vec<Vec<T>>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        let mut parsed_matrix = vec![];
        for _ in 0..lines {
            self.reader.read_line(&mut self.buffer)?;
            parsed_matrix.push(
                self.buffer
                    .trim()
                    .split_whitespace()
                    .map(|s| s.parse())
                    .collect::<Result<Vec<_>, _>>()?,
            );
            self.buffer.clear();
        }
        Ok(parsed_matrix)
    }

    #[allow(dead_code)]
    fn read_chars(&mut self) -> BoxResult<Vec<char>> {
        self.reader.read_line(&mut self.buffer)?;
        let chars = self.buffer.trim().chars().collect::<Vec<_>>();
        self.buffer.clear();
        Ok(chars)
    }
}