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)

ns = gets.chomp.split("")
ns.map!{|item|
    if item != "?" then
    item.to_i
  else
    item.to_s
  end
}
dp = Array.new(13, 0)
dp[0]=1
 
ns.each do |n|
  dpnext = Array.new(13, 0)
  dp.each_with_index {|b, num|
    if n == "?"
      10.times {|t|
        dpnext[ (num * 10 + t) % 13 ] += b
        dpnext[ (num * 10 + t) % 13 ] %= 1000000007
      }
    else
      dpnext[ (num * 10 + n) % 13 ] += b
      dpnext[ (num * 10 + n) % 13 ] %= 1000000007
    end
  }
  dp = dpnext
end
p dp[5]%1000000007