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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
#[allow(unused_imports)]
use itertools::Itertools;
#[allow(unused_imports)]
use num::*;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;
#[allow(unused_imports)]
use std::collections::*;

#[derive(Copy, Clone, Debug, Eq, PartialEq)]
pub struct ModInt(u32);

impl ModInt {
  pub const MOD: u32 = 1_000_000_007;

  pub fn inv(self) -> Self {
    if self.0 == 0 {
      panic!();
    }
    self.pow(Self::MOD - 2)
  }

  pub fn pow(self, e: u32) -> Self {
    if e == 0 {
      return Self::new(1);
    }
    let mut res = self.pow(e >> 1);
    res *= res;
    if e & 1 == 1 {
      res *= self;
    }
    res
  }

  fn new(n: i64) -> Self {
    let mut n = n % (Self::MOD as i64);
    if n.is_negative() {
      n += Self::MOD as i64;
    }
    Self(n as u32)
  }
}

impl From<i32> for ModInt {
  fn from(n: i32) -> Self {
    ModInt::from(n as i64)
  }
}

impl From<i64> for ModInt {
  fn from(n: i64) -> Self {
    Self::new(n)
  }
}

impl From<isize> for ModInt {
  fn from(n: isize) -> Self {
    ModInt::from(n as i64)
  }
}

impl From<u32> for ModInt {
  fn from(n: u32) -> Self {
    ModInt::from(n as u64)
  }
}

impl From<u64> for ModInt {
  fn from(n: u64) -> Self {
    Self::new(n as i64)
  }
}

impl From<usize> for ModInt {
  fn from(n: usize) -> Self {
    ModInt::from(n as u64)
  }
}

impl Into<i32> for ModInt {
  fn into(self) -> i32 {
    self.0 as i32
  }
}

impl Into<i64> for ModInt {
  fn into(self) -> i64 {
    self.0 as i64
  }
}

impl Into<isize> for ModInt {
  fn into(self) -> isize {
    self.0 as isize
  }
}

impl Into<u32> for ModInt {
  fn into(self) -> u32 {
    self.0
  }
}

impl Into<u64> for ModInt {
  fn into(self) -> u64 {
    self.0 as u64
  }
}

impl Into<usize> for ModInt {
  fn into(self) -> usize {
    self.0 as usize
  }
}

impl std::fmt::Display for ModInt {
  fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
    write!(f, "{}", self.0)
  }
}

impl std::ops::Add for ModInt {
  type Output = Self;

  fn add(self, rhs: Self) -> Self {
    Self::new((self.0 + rhs.0) as i64)
  }
}

impl std::ops::AddAssign for ModInt {
  fn add_assign(&mut self, rhs: Self) {
    *self = *self + rhs;
  }
}

impl std::ops::Div for ModInt {
  type Output = Self;

  fn div(self, rhs: Self) -> Self {
    self * rhs.inv()
  }
}

impl std::ops::DivAssign for ModInt {
  fn div_assign(&mut self, rhs: Self) {
    *self = *self / rhs;
  }
}

impl std::ops::Mul for ModInt {
  type Output = Self;

  fn mul(self, rhs: Self) -> Self {
    Self::new((self.0 as i64) * (rhs.0 as i64))
  }
}

impl std::ops::MulAssign for ModInt {
  fn mul_assign(&mut self, rhs: Self) {
    *self = *self * rhs;
  }
}

impl std::ops::Sub for ModInt {
  type Output = Self;

  fn sub(self, rhs: Self) -> Self {
    Self::new((self.0 as i64) - (rhs.0 as i64))
  }
}

impl std::ops::SubAssign for ModInt {
  fn sub_assign(&mut self, rhs: Self) {
    *self = *self - rhs;
  }
}

fn main() {
  input! {
    s: Chars
  };

  let p = 13;
  let mut ten_factor = 1;
  let mut dp = vec![vec![ModInt::from(0); p]; s.len() + 1];
  dp[0][0] = ModInt::from(1);
  for i in 0..s.len() {
    let ch = s[s.len() - i - 1];
    match ch {
      '?' => {
        for n in 0..=9 {
          for j in 0..p {
            let m = n * ten_factor;
            let k = (j + m) % p;
            let v = dp[i + 1][k] + dp[i][j];
            dp[i + 1][k] = v;
          }
        }
      }
      _ => {
        let n = ch.to_digit(10).unwrap() as usize;
        for j in 0..p {
          let m = n * ten_factor;
          let k = (j + m) % p;
          let v = dp[i + 1][k] + dp[i][j];
          dp[i + 1][k] = v;
        }
      }
    }
    ten_factor = (ten_factor * 10) % p;
  }
  println!("{}", dp[s.len()][5]);
}
*/

fn main() {
    let exe = "/tmp/bin62589588";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";