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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

s = gets.chomp

mod = 10 ** 9 + 7
n = s.length

dp = Array.new(13, 0)
dp[0] = 1

(1..n).each do |i|
    ch = s[i-1]
    ndp = Array.new(13, 0)
    if ch != '?'
        num = ch.to_i
        (0...13).each do |m|
            ndp[(m * 10 + num) % 13] += dp[m]
        end
    else
        (0..9).each do |num|
            (0...13).each do |m|
                ndp[(m * 10 + num) % 13] += dp[m]
            end
        end
    end
    dp = ndp.map { |x| x % mod }
end

puts dp[5]