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
s=gets
s.chomp!
s.reverse!
dp=Array.new(s.length+1){Array.new(13,0)};dp[0][0]=1

coef=1
(s.length).times do |i|
  if s[i]=='?'
    13.times do |j|
      10.times do |k|
        ind=(j+coef*k)%13
        temp=dp[i+1][ind]+dp[i][j]
        dp[i+1][ind] = temp>=MOD ? temp-MOD : temp
      end
    end
  else
    si=s[i].to_i
    13.times do |j|
      ind=(j+coef*si)%13
      temp=dp[i+1][ind]+dp[i][j]
      dp[i+1][ind] = temp>=MOD ? temp-MOD : temp
    end
  end
  coef=coef*10%13
end

puts dp[s.length][5]