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
//error_reporting(0);
$S = trim(fgets(STDIN));
//list($A,$B) =  explode(" ",trim(fgets(STDIN)));
//$B =  explode(" ",trim(fgets(STDIN)));

$len = strlen($S);

$N=13;
$dp=array_fill(0,$N,0);
$dp[0]=1;
$mod = 1000000007;
$mul = 1;

for($i=$len-1;$i>=0;$i--) {
  $nextDP = array_fill(0,$N,0);
  if ($S[$i]=='?') {
    for($k=0;$k<10;$k++) {
      for($j=0;$j<$N;$j++) {
        $nextDP[($k*$mul+$j)%$N] += $dp[$j];
        $nextDP[($k*$mul+$j)%$N] %= $mod;
      }
    }
  }
  else {
    $k = (int)$S[$i];
    for($j=0;$j<$N;$j++) {
        $nextDP[($k*$mul+$j)%$N] += $dp[$j];
        $nextDP[($k*$mul+$j)%$N] %= $mod;
    }
  }
  $mul *= 10;
  $mul %= $N;
  $dp=$nextDP;
}
printf("%d\n",$dp[5]);