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.to_s
@s_array = @s.split('').reverse
mod = [0] * 13

@s.length.times do |cnt|
  n = @s_array[cnt]
  newmod = [0] * 13
  if cnt == 0
    if n == "?"
      0.upto(9) do |l|
        mod[l] = 1
      end
    else
      mod[n.to_i] = 1
    end
  elsif n == '?'
    (0..9).each do |h|  
      m = (((10**cnt)%13)*h)%13
      13.times do |j|
        newmod[(j+m)%13] += mod[j]
      end
    end
    mod = newmod
  else
    m = (((10**cnt)%13)*n.to_i)%13
    13.times do |j|
      newmod[(j + m) % 13] = mod[j]
    end
    mod = newmod
  end
end

# print mod
print (mod[5])%(10**9+7)