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)

use std::io::*;
use std::str::FromStr;

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

const MOD: i64 = 1e+9 as i64 + 7;

fn calc(depth: usize, rest: usize, seq: &Vec<char>, memo: &mut Vec<Vec<i64>>) -> i64 {
    let n = seq.len();
    if depth == n {
        if rest == 5 {
            return 1;
        } else {
            return 0;
        }
    }
    if memo[depth][rest] != -1 {
        return memo[depth][rest];
    }
    let mut ret = 0;
    for i in 0..10 {
        if seq[depth] == '?' || (seq[depth] as u8 - '0' as u8) as usize == i {
            let nrest = (rest * 10 + i) % 13;
            ret = (ret + calc(depth + 1, nrest, seq, memo)) % MOD;
        }
    }
    memo[depth][rest] = ret;
    return ret;
}

fn main() {
    let seq = read::<String>().chars().collect::<Vec<char>>();
    let n = seq.len();
    let mut memo = vec![vec![-1; 13]; n];
    let ans = calc(0, 0, &seq, &mut memo);
    println!("{}", ans);
}