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
MOD = 10**9 + 7

d0 = [1] + [0] * 12
(0 ... S.length).each do |i|
  x = S[i]
  d1 = Array.new(13, 0)
  if x == '?'
    (0 .. 9).each do |j|
      (0 ... 13).each{|k| d1[(10*k + j) % 13] += d0[k]}
    end
  else
    j = x.to_i
    (0 ... 13).each{|k| d1[(10*k + j) % 13] += d0[k]}
  end
  d0 = d1.map{|x| x % MOD}
end
puts d0[5]