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

remainder = Array.new(13) {0}
remainder[0] = 1

ans = 0
S.chars.each_with_index do |s, i|
  digit = S.length - i - 1
  next_remainder = Array.new(13) {0}

  if s == '?'
    for i in 0..9
      d = 10**digit * i
      for j in 0..12
        next_remainder[(j + d % 13) % 13] += remainder[j]
        next_remainder[(j + d % 13) % 13] %= MOD
      end
    end
  else
    d = 10 ** digit * s.to_i
    for j in 0..12
      next_remainder[(j + d % 13) % 13] += remainder[j]
      next_remainder[(j + d % 13) % 13] %= MOD
    end
  end

  remainder = next_remainder
end

p remainder[5]