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(unused_macros)]

use std::cell::RefCell;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::fmt::{Debug, Formatter, Write as FmtWrite};
use std::io::{stderr, stdin, BufRead, Write};
use std::mem::{replace, swap};
use std::ops::*;
use std::rc::Rc;


//
// Macro debug!
//

#[cfg(debug_assertions)]
include!{"./procon/debug.rs"}

#[cfg(not(debug_assertions))]
macro_rules! debug {
    ($($arg:expr),*) => {};
}


//
// Macro input!
//

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}


//
// IteratorExt
//

trait IteratorExt: Iterator + Sized {
    fn vec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

impl<T: Iterator> IteratorExt for T {}


//
// Main
//

const C: usize = 13;
const M: i64 = (1e9 as i64) + 7;

fn main() {
    input! {
        xs: chars,
    }
    let mut xs = xs;
    xs.reverse();

    debug!(xs);

    let mut mod_10_pow = vec![0_usize; xs.len()];
    {
        let mut x = 1;
        for i in 0..xs.len() {
            mod_10_pow[i] = x;
            x *= 10;
            x %= C;
        }
    }

    let mut a: Vec<i64> = vec![0; C];
    let mut b: Vec<i64> = vec![0; C];
    let mut d = &mut a;
    let mut e = &mut b;

    for (i, x) in xs.into_iter().enumerate() {
        if i == 0 {
            if x == '?' {
                for y in 0..10 {
                    e[y] = 1;
                }
            } else {
                let y = (x as usize) - ('0' as usize);
                e[y] = 1;
            }
        } else {
            swap(d, e);
            e.clear();
            e.resize(C, 0);

            if x == '?' {
                for y in 0..10 {
                    for j in 0..C {
                        let k = (j + y * mod_10_pow[i]) % C;
                        e[k] += d[j];
                        e[k] %= M;
                    }
                }
            } else {
                let y = (x as usize) - ('0' as usize);
                
                for j in 0..C {
                    let k = (j + y * mod_10_pow[i]) % C;
                    e[k] += d[j];
                    e[k] %= M;
                }
            }
        }
    }

    println!("{}", e[5]);
}