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: Time Limit Exceeded)

use std::str::FromStr;
use std::io::stdin;

fn main() {
    let s: String = read();
    let l: usize = s.len();
    let m: usize = 1000_000_007;
    let mut dp: Vec<Vec<usize>> = Vec::with_capacity(l + 1);
    for i in 0..(l + 1) {
        dp.push(Vec::new());
        for _ in 0..13 { dp[i].push(0); }
    }
    dp[0][0] = 1;
    for i in 0..l {
        let c = s.chars().nth(i).unwrap();
        for j in (0 as usize)..(10 as usize) {
            if c != '?' && c.to_string() != j.to_string() { continue; }
            for k in (0 as usize)..(13 as usize) {
                dp[i + 1][(k * 10 + j) % 13] += dp[i][k];
            }
        }
        for j in (0 as usize)..(13 as usize) {
            dp[i + 1][j] %= m
        }
    }
    println!("{}", dp[l][5]);
}

fn read<T: FromStr>() -> T {
    let mut line = String::new();
    stdin().read_line(&mut line).ok();
    line.trim().parse().ok().unwrap()
}