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 (1.42.0) (judge verdict: Accepted)

// -*- coding:utf-8-unix -*-

#![allow(dead_code)]
#![allow(unused_imports)]

use std::cmp::*;
use std::collections::*;
use std::fs::File;
use std::io::prelude::*;
use std::io::*;
use std::vec;

const INF: i64 = 1223372036854775807;
const MEM_SIZE: usize = 202020;
const MOD: i64 = 1000000007;
// const MOD: i64 = 998244353;

use std::cmp::*;
use std::collections::*;
use std::io::stdin;
use std::io::stdout;
use std::io::Write;
#[allow(dead_code)]
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()
}

#[allow(dead_code)]
fn readi() -> (i64) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    iter.next().unwrap().parse::<i64>().unwrap()
}

#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}
#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

#[allow(dead_code)]
fn readii() -> (i64, i64) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<i64>().unwrap(),
        iter.next().unwrap().parse::<i64>().unwrap(),
    )
}

#[allow(dead_code)]
fn readiii() -> (i64, i64, i64) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<i64>().unwrap(),
        iter.next().unwrap().parse::<i64>().unwrap(),
        iter.next().unwrap().parse::<i64>().unwrap(),
    )
}
#[allow(dead_code)]
fn readuu() -> (usize, usize) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
    )
}

#[allow(dead_code)]
fn readuuu() -> (usize, usize, usize) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
    )
}

#[allow(dead_code)]
fn readuuuu() -> (usize, usize, usize, usize) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
    )
}

#[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()
        })*
    };
}

#[allow(dead_code)]
pub fn gcd(a: u64, b: u64) -> u64 {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}
#[allow(dead_code)]
pub fn lcm(a: u64, b: u64) -> u64 {
    a / gcd(a, b) * b
}
#[allow(dead_code)]
/// (gcd, x, y)
pub fn extgcd(a: i64, b: i64) -> (i64, i64, i64) {
    if b == 0 {
        (a, 1, 0)
    } else {
        let (gcd, x, y) = extgcd(b, a % b);
        (gcd, y, x - (a / b) * y)
    }
}
#[allow(dead_code)]
/// x ^ n % m
pub fn mod_pow(x: usize, n: usize, m: usize) -> usize {
    let mut res = 1;
    let mut x = x % m;
    let mut n = n;
    while n > 0 {
        if n & 1 == 1 {
            res = (res * x) % m;
        }
        x = (x * x) % m;
        n >>= 1;
    }
    res
}
#[allow(dead_code)]
pub fn mod_inverse(a: u64, m: u64) -> u64 {
    let (_, x, _) = extgcd(a as i64, m as i64);
    ((m as i64 + x) as u64 % m) % m
}
#[allow(dead_code)]
pub fn fact_table(len: usize, m: u64) -> Vec<u64> {
    let mut res = vec![1; len + 1];
    for i in 1..len + 1 {
        res[i] = (i as u64 * res[i - 1]) % m;
    }
    res
}
#[allow(dead_code)]
/// Factorial and Inverse factorial table
pub fn fact_inv_table(size: usize, m: u64) -> (Vec<u64>, Vec<u64>) {
    let mut fact = vec![1; size];
    let mut fact_inv = vec![1; size];
    for i in 2..size {
        fact[i] = fact[i - 1] * i as u64 % m;
        fact_inv[i] = m - ((m / i as u64) * fact_inv[(m % i as u64) as usize] % m);
    }
    for i in 1..size {
        fact_inv[i] = fact_inv[i - 1] * fact_inv[i] % m;
    }
    (fact, fact_inv)
}
#[allow(dead_code)]
/// (a mod p, e when n! = a p\^e)
pub fn mod_fact(n: u64, p: u64, fact: &[u64]) -> (u64, u64) {
    if n == 0 {
        (1, 0)
    } else {
        let (a, b) = mod_fact(n / p, p, fact);
        let pow = b + n / p;
        if n / p % 2 != 0 {
            (a * (p - fact[(n % p) as usize]) % p, pow)
        } else {
            (a * fact[(n % p) as usize] % p, pow)
        }
    }
}
#[allow(dead_code)]
/// C(n, k) % p
pub fn mod_comb(n: u64, k: u64, p: u64, fact: &[u64]) -> u64 {
    if n < k {
        0
    } else {
        let (a1, e1) = mod_fact(n, p, fact);
        let (a2, e2) = mod_fact(k, p, fact);
        let (a3, e3) = mod_fact(n - k, p, fact);
        if e1 > e2 + e3 {
            0
        } else {
            a1 * mod_inverse(a2 * a3 % p, p) % p
        }
    }
}
#[allow(dead_code)]
/// H(n, k) % p
pub fn mod_comb_repetition(n: u64, k: u64, p: u64, fact: &[u64]) -> u64 {
    mod_comb(n - 1 + k, n - 1, p, fact)
}

fn solve() {
    let s: String = read();
    let mut v = s.as_bytes().to_vec();
    for i in 0..v.len() {
        if (v[i] == '?' as u8) {
            v[i] = 10;
        } else {
            v[i] -= '0' as u8;
        }
    }
    v.reverse();
    // let mut dp: Vec<usize> = vec![0];
    let mut dp = vec![vec![0 as usize; (13) as usize]; (v.len() + 1) as usize];
    dp[0][0] = 1;
    for i in 0..v.len() {
        let mut x = mod_pow(10, i, 13);
        if (v[i] != 10) {
            for z in 0..13 {
                let mut nx = (x * v[i] as usize + z as usize) % 13;
                dp[i + 1][nx] += dp[i][z];
                dp[i + 1][nx] %= MOD as usize;
            }
        } else {
            for z in 0..13 {
                for zz in 0..10 {
                    let mut nx = (x * zz + z as usize) % 13;
                    dp[i + 1][nx] += dp[i][z];
                    dp[i + 1][nx] %= MOD as usize;
                }
            }
        }
    }

    println!("{}", dp[v.len()][5]);
}
fn main() {
    solve()
}