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.to_s
@s_array = @s.split('')
@digit = @s_array.size
max_value = @s.gsub('?', "9").to_i

max_cnt = (max_value - 5)/13

# puts max_value
# puts max_cnt


# @return Boolean
def valid?(str)
  n_array = str.split('')
  @s_array.each_with_index do |s, i|
    next if s == '?'
    return false if s != n_array[i]
  end
  true
end

@cnt = 0
1.upto(max_cnt) do |i|
  target_number = (i*13+5)
  target_digit = target_number.to_s.length
  diff_digit = @digit - target_digit
  target_str = "0"*diff_digit + target_number.to_s
  @cnt += 1 if valid?(target_str)
end

puts @cnt % ((10**9)+7)