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 (2.7.1) (judge verdict: Time Limit Exceeded)

MOD = 10 ** 9 + 7

s = gets.chomp.chars
n = s.size
dp = Array.new(n) { Hash.new(0) }

n.times do |i|
  if i == 0
    if s[i] == "?"
      (0..9).each do |c|
        dp[i][c] = 1
      end
    else
      dp[i][s[i].to_i] = 1
    end
  else
    m = dp[i - 1].keys
    m.each do |k|
      if s[i] != "?"
        j = (10 * k + s[i].to_i) % 13
        dp[i][j] = (dp[i][j] + dp[i - 1][k]) % MOD
      else
        (0..9).each do |c|
          j = (10 * k + c) % 13
          dp[i][j] = (dp[i][j] + dp[i - 1][k]) % MOD
        end
      end
    end
  end
end
puts dp[n - 1][5]