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(dead_code)]
use std::io::prelude::*;
use std::cmp::{max, min};

const MOD: i64 = 1e9 as i64 + 7; 

fn main(){
    let s: Vec<char> = read::<String>().chars().collect();
    let n: usize = s.len();
    let mut dp: Vec<Vec<i64>> = vec![vec![0; 14]; n + 1];
    dp[0][0] = 1;
    for i in 0..n{
        for j in 0..14{
            if s[i] == '?'{
                for k in 0..10{
                    dp[i + 1][(j * 10 + k) % 13] += dp[i][j];
                    dp[i + 1][(j * 10 + k) % 13] %= MOD;
                }
            }else{
                let t: usize = (j * 10 + s[i] as usize - '0' as usize) % 13;
                dp[i + 1][t] += dp[i][j];
                dp[i + 1][t] %= MOD;
            }
        }
    }
    println!("{}", dp[n][5]);
}

fn upper_bound(a: &Vec<i32>, x: &i32) -> Option<usize>
{
    let mut ok: isize = a.len() as isize;
    let mut ng: isize = -1;
    if ok == 0 || a[ok as usize - 1] <= *x{
        None
    }else{
        while (ng - ok).abs() > 1{
            let mid = (ok + ng) / 2;
            if a[mid as usize] > *x{
                ok = mid;
            }else{
                ng = mid;
            }
        }
        Some(ok as usize)
    }
}

fn read<T>() -> T
where
    T: std::str::FromStr,
{
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}