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)

use std::io::prelude::*;

fn mod_add(x: u64, y: u64) -> u64 {
    (x + y) % (1_000_000_007)
}

fn main() {
    let mut input_str = String::new();
    std::io::stdin().read_to_string(&mut input_str).unwrap();

    let input_parts = input_str.split_whitespace().collect::<Vec<_>>();
    let mut input_parts_it = input_parts.iter().cloned();

    let s: Vec<char> = input_parts_it.next().unwrap().chars().rev().collect();

    let mut perms = vec![0u64; 13];
    perms[0] = 1;

    let mut factor = 1;

    for &digit in s.iter() {
        if digit == '?' {
            let mut perms2 = vec![0u64; 13];
            for val in 0..10 {
                let shift = (val * factor) % 13;
                for rem in 0..13 {
                    perms2[rem] = mod_add(perms2[rem], perms[(rem + 13 - shift) % 13]);
                }
            }
            perms = perms2;
        } else {
            let val = digit as usize - '0' as usize;
            let shift = (val * factor) % 13;
            perms = (0..13).map(|rem| perms[(rem + 13 - shift) % 13]).collect();
        }

        factor = (factor * 10) % 13;
    }

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