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=10**9+7
io = STDIN
s=io.gets.chomp
m,n=s.size,13
dp=Array.new(n,0)
dp[0]=1
m.times do |i|
  nextdp=Array.new(n,0)
  digit=10**i
  n.times{|j|nextdp[j]=0}
  if s[-1-i]=="?"
    10.times do |k|
      n.times do |j|
        ix=(k*digit+j)%n
        nextdp[ix]+=dp[j]
        nextdp[ix]%=mod
      end
    end
  else
    k=s[-1-i].to_i
    n.times do |j|
      ix=(k*digit+j)%n
      nextdp[ix]+=dp[j]
      nextdp[ix]%=mod
    end
  end
  dp=nextdp
end
p dp[5]