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
const N = 13;
const MOD = 10 ** 9 + 7;

# 入力
fscanf(STDIN, '%s', $s);
$s_arr = str_split($s);
$n = count($s_arr);

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

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