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.chomp.split("").reverse
dp=Array.new(s.size+1).map{Array.new(13,0)}
dp[0][0] = 1
s.each_with_index do |c,i|
  l = 10**i % 13

  if c == '?'
    0.upto(9) do |k|
      m = k.to_i * l % 13
      0.upto(12) do |j|
        mm = (j + m) % 13
        dp[i+1][mm] += dp[i][j]
        dp[i+1][mm] %= MOD
      end
    end

  else
    m = c.to_i * l % 13
    0.upto(12) do |j|
      mm = (j + m) % 13
      dp[i+1][mm] += dp[i][j]
      dp[i+1][mm] %= MOD
    end
  end
end
p dp[s.size][5]