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)

s = gets.chomp
div = 1000000007

dp = []
100005.times do |i|
  dp[i] = [0,0,0,0,0,0,0,0,0,0,0,0,0]
end
dp[0][0] = 1

len = s.size
len.times do |i|
  c = s[i].to_i if s[i] != "?"
  c = -1        if s[i] == "?"
  10.times do |j|
    next if (c != -1 && c != j)
    13.times do |ki|
      dp[i+1][(ki*10+j)%13] += dp[i][ki]
    end
  end
  13.times do |j|
    dp[i+1][j] %= div
  end
end

puts dp[len][5]