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_imports)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num::clamp;
use proconio::{input, marker::*, fastout};
use superslice::*;

#[fastout()]
fn main() {
    input! {
        s: Bytes
    }
    let m = 1000000007usize;

    let mut dp = vec![vec![0usize; 13]; s.len()+1];
    dp[0][0] = 1;
    for i in 0..s.len() {
        for prev in 0..13 {
            if s[i] != b'?' {
                let v = prev * 10 + (s[i] - b'0') as usize;
                let r = v % 13;
                dp[i+1][r as usize] += dp[i][prev];
                dp[i+1][r as usize] %= m;
                continue;
            }
            for d in 0..=9 {
                let v = prev * 10 + d;
                let r = v % 13;
                dp[i+1][r as usize] += dp[i][prev];
                dp[i+1][r as usize] %= m;
            }
        }
    }
    let ans = dp[s.len()][5];
    println!("{}", ans);
}