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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php

  list($s) = explode(" ", trim(fgets(STDIN)));

//  $s = str_repeat("?", 100000);
  $n = strlen($s);

  $s = strrev($s);
  $s = str_split($s);

  $mod = 1000000007;

  $dp = [];
  $dp[0] = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
  $mul = 1;

  for ($i=0; $i<$n; ++$i) {
    $dp[$i+1] = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
    if($s[$i] === '?'){
      for($k=0; $k<10; $k++){
        $diff = $mul * $k % 13;
        for($j=0; $j<13; ++$j){
          $dp[$i+1][($diff+$j)%13] += $dp[$i][$j];
        }
      }
    }else{
      $diff = $mul * $s[$i] % 13;
      for($j=0; $j<13; $j++){
        $dp[$i+1][($diff+$j)%13] += $dp[$i][$j];
      }
    }
    for($k=0; $k<13; $k++){
      $dp[$i+1][$k] %= $mod;
    }
    $mul = $mul * 10 % 13;
  }
//var_dump($dp);

  echo $dp[$n][5];