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: Wrong Answer)

s = gets.chomp!.split("").map{|x| x == '?' ? -1 : x.to_i}
l = s.size
dp = Array.new(l+1).map{Array.new(13,0)}
dp[0][0] = 1

l.times do |i|
    c = s[i]
    10.times do |key|
        if c == -1 || c == key then
            13.times do |j|
                dp[i+1][(j*10+key) % 13] += dp[i][j] % (10 ** 9 + 7) 
            end
        end
    end
    p dp[i+1]
end

puts dp[l][5] % (10 ** 9 + 7)