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

n = [1, 10, 9, 12, 3, 4]
N = n.length

# dp[i][j] : 数
#   i : 桁
#   j : あまり
dp = Array.new(s.length+1).map{Array.new(13, 0)}

dp[0][0] = 1

s.reverse!
s.chars.each_with_index do |c, i|
    for j in 0...13
        if c == "?"
            10.times do |cc|
                x = (j + cc * n[i%N]) % 13
                dp[i+1][x] = (dp[i+1][x] + dp[i][j]) % 1000000007
            end
        else
            x = (j + c.to_i * n[i%N]) % 13
            dp[i+1][x] = (dp[i+1][x] + dp[i][j]) % 1000000007
        end
    end
end

puts dp[s.length][5]