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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::io::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed reading char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed parsing")
}

fn main() {
    
    const M : u64 = 1_000_000_007;
    
    const N : usize = 13;
    
    let s : Vec<char> = read::<String>().chars().collect();

    let mut dp = [0; N];
    dp[0] = 1;
    
    for item in s {
        let mut next_dp = [0; N];
        
        if item == '?'{
            // ? = 0..10
            for i in 0..10 {
                for j in 0..N {
                    next_dp[ ((j * 10) + i) % N] += dp[j];
                    next_dp[ ((j * 10) + i) % N] %= M;
                }
            }
        }
        
        else {
            let i = item as usize - '0' as usize;
            
            for j in 0..N {
                next_dp[ ((j * 10) + i) % N] += dp[j];
                next_dp[ ((j * 10) + i) % N] %= M;
            }
        }
 
        // copy dp
        for i in 0..N{
            dp[i] = next_dp[i];
        }
    }
    
    println!("{}", dp[5]);
    
}