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 PHP (5.6.30) (judge verdict: Runtime Error)

<?php
  $arr = explode(" ", trim(fgets(STDIN)));
  $question_count = count(array_keys($arr, "?"));
  
  $max = "";
  for($i = 0; $i < $question; $i++) {
    $max .= "9";
  }
  
  $matrix = [];
  for($i = 0; $i < $question_count; $i++) {
    $matrix[$i] = 0;
  }

  $index = $question_count;
  function createNumber($arr) {
    $str = '';
    foreach($arr as $value) {
      if($value === "?") {
        $str .= $matrix[$index];
        $index--;
      } else {
        $str .= $value;
      }
    }
    return (int)$str;
  }

  function check($input) {
	$number = (int)implode($input);
    return ($number % 13 === 5);
  }
    
  function increment($input) {
    $number = (int)implode($input);
    $number++;
    $tmp = str_split((string)$number);
    
    $res = [];
    for($i = $question_count; $i >= 0: $i--) {
      if(array_key_exists($i, $tmp)) {
        $res[$i] = $tmp[$i];
      } else {
        $res[$i] = 0;
      }
    }
    
    return $res;
  }

  $answer = 0;
  while((int)$max >= (int)implode($matrix)) {
  	$tmp = createNumber($matrix);
    if(check($tmp)) $answer++;
    $matrix = $increment($matrix)
  }

  echo $answer % (pow(10, 9) + 7);