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: Accepted)

<?php
  $res = 1000000007;
  $s = str_split(trim(fgets(STDIN)));
  $n = count($s);
  for($i=0;$i<13;$i++){
    $dp[$i] = 0;
    $ndp[$i] = 0;
  }
  $dp[0] = 1;
  $keta = 1;
  for($i=$n-1;$i>=0;$i--){
    if($s[$i]=="?"){
      for($j=0;$j<=9;$j++){
        for($l=0;$l<13;$l++){
          $ndp[(($j*$keta+$l)%13)] += $dp[$l]%$res;
          //if($i!=$n-1)echo($j."?-".(($j*$keta+$l)%13)."=".$dp[$l]."/");
        }
      }
      //echo("ndpの結果:");
      for($j=0;$j<13;$j++){
        //echo($ndp[$j].".");
        $dp[$j] = $ndp[$j]%$res;
        $ndp[$j] = 0;
      }
    }else{
      for($j=0;$j<13;$j++){
        //echo(($s[$i]*($keta%13)+$j)%13);
        //echo("/");
        $ndp[(($s[$i]*$keta+$j)%13)] += $dp[$j]%$res;
      }
      for($j=0;$j<13;$j++){
        $dp[$j] = $ndp[$j]%$res;
        $ndp[$j] = 0;
      }
    }

    $keta = ($keta*10)%13;
    //echo("for文のi=".$i."終了後\n");
    //for($j=0;$j<13;$j++){
    //  echo("/dp[".$j."]=".$dp[$j]."/");
    //}
    //echo("\n");
  }
  echo($dp[5]%$res);