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 OCaml (4.02.3) (judge verdict: Accepted)

let m = 1000000007
let ( +^ ) x y = (x + y) mod m

let () =
  let s = read_line () in
  let dp = Array.make_matrix (String.length s + 1) 13 0 in
  dp.(0).(0) <- 1;
  String.iteri (fun i ->
    let go n =
      for j = 0 to 12 do
        dp.(i + 1).((10 * j + n) mod 13) <-
          dp.(i + 1).((10 * j + n) mod 13) +^ dp.(i).(j)
      done in
    function
      | '?' ->
          for i = 0 to 9 do
            go i
          done
      | c -> go (int_of_char c - int_of_char '0')) s;
  Printf.printf "%d\n" dp.(String.length s).(5)