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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]

use proconio::{input, fastout};
use proconio::marker::*;
use std::mem::swap;

#[fastout]
fn main() {
    input! {
    s: Chars
    }
    let p = 1_000_000_007;
    let n = s.len();
    let mut dp = vec![0; 13];
    dp[0] = 1;
    for i in 0..n {
        let mut prev = vec![0; 13];
        swap(&mut prev, &mut dp);
        let d = if s[i] == '?' { 10 } else { s[i].to_digit(10).unwrap() as usize };
        for j in 0..10{
            if d < 10 && j != d {continue}
            for k in 0..13 {
                dp[(k * 10 + j) % 13] += prev[k];
                dp[(k * 10 + j) % 13] %= p;
            }
        }
    }
    let ans = dp[5];
    println!("{}", ans);
}