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)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

const MOD: u64 = 1000000000 + 7;

fn pow(i: u32) -> usize {
    let mut res = 1;
    for _ in 1..i+1 {
        res = (res * 10) % 13;
    }
    res
}

fn solve(mut s: Vec<char>) -> u64 {
    s.reverse();

    let mut dp = vec![vec![0; 13]; s.len()];
    if s[0] == '?' {
        for i in 0..10 {
            dp[0][i] = 1 as u64;
        }
    } else {
        let n = s[0].to_digit(10).unwrap() as usize;
        dp[0][n] = 1 as u64;
    }

    for i in 1..s.len() {
        let pow = pow(i as u32);
        if s[i] == '?' {
            for j in 0..10 {
                for k in 0..13 {
                    let rem = (k + pow * j) % 13;
                    dp[i][rem] += dp[i-1][k] % MOD;
                }
            }
        } else {
            for k in 0..13 {
                let n = s[i].to_digit(10).unwrap() as usize;
                let rem = (k + pow * n)  % 13;
                dp[i][rem] += dp[i-1][k] % MOD;
            }
        }
    }

    dp[s.len()-1][5] % MOD
}


fn main() {
    input! {
        s: chars
    };
    println!("{}", solve(s));
}