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)

use proconio::input;

const MOD: usize = 1_000_000_007;

fn main() {
  input! {
    s: String,
  }
  let n = 13;
  let mut chars = s.chars().collect::<Vec<char>>();
  let mut dp = vec![0;n];
  dp[0] = 1;

  let mut mul = 1;
  let mut index = chars.len() - 1;
  loop {
    let c = chars[index];
    let mut next_dp = vec![0;n];
    if c == '?' {
      for i in 0..10 {
        for ii in 0..n {
          next_dp[(i * mul + ii) % n] += dp[ii];
          next_dp[(i * mul + ii) % n] %= MOD;
        }
      }
    } else {
      let i = c.to_digit(10).unwrap() as usize;
      for ii in 0..n {
        next_dp[(i * mul + ii) % n] += dp[ii];
        next_dp[(i * mul + ii) % n] %= MOD;
      }
    }
    mul *= 10;
    mul %= n;
    dp = next_dp;
    
    if index == 0 {
      break
    }
    index -= 1;
  }
  
  println!("{}", dp[5]);
}