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(dead_code)]
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}
#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}
#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}
#[allow(dead_code)]
fn yn(result: bool) {
    if result {
        println!("Yes");
    } else {
        println!("No");
    }
}

fn main() {
    let s = read::<String>().chars().collect::<Vec<char>>();
    let n = s.len() as usize;

    let mut dp = vec![vec![0i64; 13]; n];

    for i in 0..n {
        if i == 0 {
            if s[i] == '?' {
                for j in 0..10 {
                    dp[i][j] = 1;
                }
            } else {
                let c = s[i] as usize - '0' as usize;
                for j in 0..13 {
                    if j == c {
                        dp[i][j] = 1;
                    }
                }
            }
        } else {
            if s[i] == '?' {
                for j in 0..10 {
                    for k in 0..13 {
                        if dp[i - 1][k] != -1 {
                            dp[i][(k * 10 + j) % 13] += dp[i - 1][k]
                        }
                    }
                }
            } else {
                let c = s[i] as usize - '0' as usize;
                for k in 0..13 {
                    if dp[i - 1][k] != -1 {
                        dp[i][(k * 10 + c) % 13] += dp[i - 1][k];
                    }
                }
            }
        }

        for j in 0..13 {
            dp[i][j] %= 1000000007;
            //println!("({}, {}): {}", i, j, dp[i][j]);
        }
    }
    println!("{}", dp[n - 1][5]);
}