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)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [$t:tt]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}


#[cfg(debug_assertions)]
macro_rules! mydbg {
    //($arg:expr) => (dbg!($arg))
    ($arg:expr) => (println!("{:?}",$arg));
}


#[cfg(not(debug_assertions))]
macro_rules! mydbg {
    ($($arg:expr),*) => {};
}


use std::cmp;
use std::collections::HashMap;



use std::ops::{ Add, Sub , Div , Mul };
static global_mod : i64 = 1000000007;

#[derive(Debug,Copy,Clone)]
pub struct ModInt {
    x : i64
}

impl ModInt{
    pub fn  new (p:i64) -> Self {
        let a = (p % global_mod + global_mod)% global_mod;     
        return ModInt{x:a};
    }

    pub fn inv (self) -> Self{
        return self.pow(global_mod-2);

    }

    pub fn pow (self , t:i64) -> Self{
        if(t==0 ) {return ModInt::new(1)};
        let mut a = self.pow(t>>1);
        a = a*a;
        if(t&1 != 0) {a = a* self};
        return a;
    }
}
impl Add for ModInt {
    type Output = ModInt;
    fn add(self,other : ModInt) -> ModInt{
        let ret  = self.x + other.x ;
        return ModInt::new(ret);
    }
}
impl Sub for ModInt {
    type Output = ModInt;
    fn sub(self,other : ModInt) -> ModInt{
        let ret  = self.x - other.x;
        return ModInt::new(ret);
    }
}
impl Mul for ModInt {
    type Output = ModInt;
    fn mul(self,other : ModInt) -> ModInt{
        let ret  = self.x * other.x ;
        return ModInt::new(ret);
    }
}

impl Div for ModInt {
    type Output = ModInt;
    fn div(self,other : ModInt) -> ModInt{
        let ret  = self.x * other.inv().x;
       return ModInt::new(ret);
    }
}

impl std::string::ToString for ModInt{
    fn to_string(&self) -> String{
        return self.x.to_string();
    }
}


pub struct Combination{
    fact : Vec<ModInt>,
    ifact : Vec<ModInt>
}

impl Combination{
    pub fn new(n:i32)->Self{
        let mut fact = vec![ModInt::new(0);(n+1) as usize];
        let mut ifact = vec![ModInt::new(0);(n+1) as usize];
        fact[0] = ModInt::new(1);
        for i in 1..n+1 { fact[i as usize] = fact[(i-1) as usize] * ModInt::new(i as i64) };
        ifact[n as usize] = fact[n as usize].inv();
        for i in (1..n+1).rev(){ ifact[(i-1) as usize] = ifact[i as usize]* ModInt::new(i as i64) }


        let a = Combination{
            fact : fact,
            ifact : ifact
        };
        return a;
    }

    pub fn gen(self , n:i32 , k:i32)-> ModInt{
        mydbg!(self.fact[n as usize]);
        mydbg!(self.ifact[k as usize]);
        mydbg!(self.ifact[(n-k) as usize]);
        if (k < 0 || k > n) {return ModInt::new(0 as i64)};
        return self.fact[n as usize]*self.ifact[k as usize]*self.ifact[(n-k) as usize];

    }
}




fn main() {


  input! { 
         s: chars
    }

    
    let n = 13i32;
    let mod7 = 10i64.pow(9)+7;
    mydbg!(mod7);
    let mut dp = vec![vec![0i64;n as usize];s.len()+1];
    dp[0][0] = 1;
    let mut mul = 1i32;
    for i in 0..s.len(){
        let index = s.len()-i-1;
        //mydbg!(s[index]);
        if s[index]=='?' {
            for k in 0..10{
                for j in 0..n{
                    dp[i+1][((k*mul + j as i32) % n) as usize] += dp[i][j as usize];
                    dp[i+1][((k*mul + j as i32) % n) as usize] %= mod7;
                }
            }
        }
        else{
            let k : i32  = s[index] as i32 - '0' as i32;
            for j in 0..n{
                dp[i+1][((k*mul + j as i32) % n) as usize] += dp[i][j as usize];
                dp[i+1][((k*mul + j as i32) % n) as usize] %= mod7;
            }
        }

        //mydbg!(dp[i+1]);
        mul = (mul * 10) % n;


    }

    
    println!("{}",dp[s.len()][5]);


}