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)

def dd
    s = gets.chomp#.to_i#.map{|x| x.to_i}
    h = s.count('?')

    cnt = 0
    for i in 0..('9'*h).to_i
        j = sprintf("%0*d", h, i).split(//)#.map{|x| x.to_i}
        l = 0
        t = s.dup
        for k in 0..(s.length-1)
            if t[k] == '?'
                t[k] = j[l]
                l += 1
            end
        end
        cnt += 1 if t.to_i%13 == 5
    end

    puts cnt
end

dd