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)

fn read_stdin() -> String {
    use std::io::Read;
    let mut input = String::new();
    std::io::stdin().read_to_string(&mut input).unwrap();
    input
}

fn scan<'a, I: Iterator<Item = &'a str>, T: std::str::FromStr>(tokens: &mut I) -> T {
    tokens.next().unwrap().parse().ok().unwrap()
}

fn main() {
    let input = read_stdin();
    let tokens = &mut input.split_whitespace();
    let s: String = scan(tokens);
    let modulo: usize = 1_000_000_007;
    let mut dp = vec![0; 13];
    dp[0] = 1;
    let mut tmp = vec![0; 13];
    for b in s.bytes() {
        if b == b'?' {
            for i in 0..13 {
                tmp[i] = 0;
            }
            for i in 0..13 {
                for b in 0..10 {
                    tmp[(i * 10 + b) % 13] += dp[i];
                }
            }
            for i in 0..13 {
                tmp[i] %= modulo;
            }
        } else {
            let b = (b - b'0') as usize;
            for i in 0..13 {
                tmp[(i * 10 + b) % 13] = dp[i];
            }
        }
        std::mem::swap(&mut dp, &mut tmp);
    }
    println!("{}", dp[5]);
}