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_variables)]
#![allow(unused_imports)]
#![allow(dead_code)]
use std::io;
use std::str::FromStr;
use std::iter::FromIterator;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::mem::{replace, swap};

const BIGINT: i64 = 1e9 as i64 + 7;

// [NOTE] つかうときには trim() 入れないと RE になるので注意
// abcde
fn read_as_line() -> String {
    let mut line = String::new();
    io::stdin().read_line(&mut line).unwrap();
    line
}

// #.#.###..
fn read_as_chars<T: FromIterator<char>>() -> T {
    let s = read_as_line();
    s.trim().chars().collect()
}

fn length_in_base2(x: usize) -> usize {
    let mut x = x;
    let mut ans = 0;
    while x > 0 {
        ans += 1;
        x >>= 1;
    }
    ans
}

fn powmod(x: i64, y: usize, z: i64) -> i64 {
    let mut ans = 1_i64;
    let mut px = x;
    let y_size = length_in_base2(y);
    for i in 0..y_size {
        if (y >> i) & 1 == 1 {
            ans = (ans * px) % z;
        }
        px = (px * px) % z;
    }
    ans
}

fn main() {
    let s: Vec<char> = read_as_chars();
    let mut xs: Vec<i64> = vec![0; 13];
    xs[0] = 1;

    for (p, &c) in s.iter().rev().enumerate() {
        let powpow = powmod(10, p, 13) as usize;
        let mut ys: Vec<i64> = vec![0; 13];
        if c == '?' {
            for k in 0..13 {
                for i in 0..10 {
                    let idx = (powpow * i + k) % 13;
                    ys[idx] = (ys[idx] + xs[k]) % BIGINT;
                }
            }
        } else {
            let n: usize = c.to_digit(10).unwrap() as usize;
            for k in 0..13 {
                let idx = (powpow * n + k) % 13;
                ys[idx] = xs[k];
            }
        }
        xs = ys;
    }
    println!("{}", xs[5]);

}