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: Time Limit Exceeded)

<?php
fscanf(STDIN, "%s", $s);

Preg_match_all('/[0-9]{0,9}|[\?]/', $s, $sList);
$pattern[0]=1;

for($i=0; $i<count($sList[0]); $i++){
  $tmp=array_fill(0,13,0);
  $pattern=array_diff($pattern, array(0));
  if($sList[0][$i]=='?'){
    foreach($pattern as $k => $v){
      for($m=0; $m<10; $m++){
        $j=$k.$m;
        $tmp[$j%13]+=$v%1000000007;
      }
    }
  }else{
    foreach($pattern as $k => $v){
      $j=$k.$sList[0][$i];
      $tmp[$j%13]+=$v%1000000007;
    }
  }
  $pattern=$tmp;
}
echo $pattern[5]%1000000007;