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)

MOD = 1_000_000_007

s = gets.rstrip

# count div 13
dp = Array.new(13, 0)
dp[0] = 1

s.length.times do |i|
  if s[i] == '?'
    newdp = Array.new(13, 0)

    10.times do |x|
      13.times do |i|
        newdp[(10 * i + x) % 13] += dp[i]
      end
    end
    dp = newdp.map {|x| x % MOD }
  else
    digit = s[i].to_i
    newdp = Array.new(13)

    13.times do |i|
      newdp[(10 * i + digit) % 13] = dp[i]
    end
    dp = newdp
  end
end

p dp[5]