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::{stdin, stdout, BufReader, BufRead, StdinLock, Write, BufWriter};

fn main() {
    let MOD = 1000000007;
    let (std_in, std_out) = (stdin(), stdout());
    let mut br = BufReader::new(std_in.lock());
    let mut bw = BufWriter::new(std_out.lock());
    
    let s = rs(&mut br);
    let n = s.len();

    let mut p = Vec::new();
    p.push(1);
    for i in 1..n {
        let x = p[i-1];
        p.push((10 * x) % 13);
    }
    p.reverse();

    let mut dp = [[0; 13]; 100005];
    dp[0][0] = 1;
    for i in 0..n {
        if (s[i] == '?') {
            for k in 0..10 {
                let x = (k * p[i]) % 13;
                for m in 0..13 {
                    dp[i+1][(m+x)%13] += dp[i][m];
                    dp[i+1][(m+x)%13] %= MOD;
                }
            }
        } else {
            let x = ((s[i] as usize - 48) * p[i]) % 13;
            for m in 0..13 {
                dp[i+1][(m+x)%13] += dp[i][m];
                dp[i+1][(m+x)%13] %= MOD;
            }
        }
    }
    writeln!(&mut bw, "{}", dp[n][5]);
}


//////////////////////////////////////////////////////////////////////////////////
#[allow(dead_code)]
fn rs(br: &mut BufReader<StdinLock>) -> Vec<char> {
    let mut buf = String::new();
    br.read_line(&mut buf).ok();
    buf.trim().chars().collect()
}

#[allow(dead_code)]
fn rn<T: std::str::FromStr>(br: &mut BufReader<StdinLock>) -> T {
    let mut buf = String::new();
    br.read_line(&mut buf).ok();
    buf.trim().parse().ok().unwrap()
}

#[allow(dead_code)]
fn rvs(br: &mut BufReader<StdinLock>) -> Vec<Vec<char>> {
    let mut buf = String::new();
    br.read_line(&mut buf).ok();
    buf.trim().split_whitespace().map(|e| e.chars().collect()).collect()
}

#[allow(dead_code)]
fn rvn<T: std::str::FromStr>(br: &mut BufReader<StdinLock>) -> Vec<T> {
    let mut buf = String::new();
    br.read_line(&mut buf).ok();
    buf.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}