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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::Chars;
#[allow(unused_imports)]
use std::collections::{VecDeque, HashMap, HashSet, BinaryHeap};

const MOD_N: u64 = 1000000007;

fn update_dp(dp: &mut Vec<Vec<u64>>, i: usize, n: u64, base_exp: u64, mod_n: u64) {
    let x = n * base_exp % mod_n;

    for j in 0..(mod_n as usize) {
        let digit_mod = ((j as u64 + x) % mod_n) as usize;
        dp[i+1][digit_mod] += dp[i][j];
        dp[i+1][digit_mod] %= MOD_N;
    }
}

fn main() {
    input! {
        s: Chars,
    }

    let mod_n = 13u64;

    // 10^n(mod13)
    let base_exp_s = vec![1u64, 10, 9, 12, 3, 4];

    let mut dp = vec![vec![0u64; mod_n as usize]; s.len()+1];
    dp[0][0] = 1;

    for (i, &c) in s.iter().enumerate() {
        let base_exp = base_exp_s[(s.len() - i - 1) % base_exp_s.len()];

        if c == '?' {
            for n in 0..10 {
                update_dp(&mut dp, i, n as u64, base_exp, mod_n);
            }
        } else {
            let n = c.to_digit(10).unwrap() as u64;
            update_dp(&mut dp, i, n, base_exp, mod_n);
        }
    }

    /*
    for i in 0..s.len()+1 {
        for j in 0..mod_n as usize {
            println!("dp[{}][{:>2}]: {}", i, j, dp[i][j]);
        }
    }
    // */

    println!("{}", dp[s.len()][5]);
}
*/

fn main() {
    let exe = "/tmp/binB8CBF41B";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";