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, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

#[fastout]
fn main() {
    input! {//
        mut s:Chars,
    }
    let n = s.len();

    //5  mod 13
    let mut dp = vec![vec![0; 13]; n + 1];

    s.reverse();
    if s[0] == '?' {
        for i in 0..=9 {
            dp[0][i] = 1;
        }
    } else {
        dp[0][charconv(s[0], '0')] = 1;
    }
    let mut keta = 10;
    for i in 1..n {
        if s[i] == '?' {
            for j in 0..=9 {
                for k in 0..13 {
                    let mm = (k + j * keta) % 13;
                    dp[i][mm] += dp[i - 1][k];
                    dp[i][mm] %= MOD;
                }
            }
        } else {
            let nm = charconv(s[i], '0');
            for k in 0..13 {
                let mm = (k + nm * keta) % 13;
                dp[i][mm] += dp[i - 1][k];
                dp[i][mm] %= MOD;
            }
        }
        keta = (keta * 10) % 13;
    }
    let mut ans = 0;
    // for i in 0..13 {
    //     ans += dp[n - 1][i];
    // }
    println!("{}", dp[n - 1][5]);
}
const MOD: usize = 1000000007;
pub fn charconv(c: char, base: char) -> usize {
    return (c as u8 - base as u8) as usize;
}