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: Time Limit Exceeded)

<?php
define("MOD", 10 ** 9 + 7);

# 入力
fscanf(STDIN, '%s', $s);
$s = strrev($s);
$n = strlen($s);

$dp[0][0] = 1;
$mul = 1;
for ($i = 0; $i < $n; $i++) {
    if ($s[$i] === '?') {
        for ($j = 0; $j < 10; $j++) {
            $diff = $mul * $j;
            for ($k = 0; $k < 13; $k++) {
                $dp[$i + 1][($diff + $k) % 13] += $dp[$i][$k];
            }
        }
    } else {
        $j = intval($s[$i]);
        $diff = $mul * $j;
        for ($k = 0; $k < 13; $k++) {
            $dp[$i + 1][($diff + $k) % 13] = $dp[$i][$k];
        }
    }
    for($k = 0; $k < 13; $k++) {
        $dp[$i + 1][$k] %= MOD;
    }
    $mul *= 10;
    $mul %= 13;
}
echo $dp[$n][5].PHP_EOL;