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

N = 13

mod = 10**9 + 7

dp = Array.new(s.length + 1) { Array.new(N) { 0 } }

dp[s.length][0] = 1
mul = 1

(s.size - 1).downto(0) do |i|
  c = s[i]

  if c == '?'
    10.times do |j|
      13.times do |k|
        dp[i][(j * mul + k) % N] += dp[i + 1][k]
      end
    end
  else
    13.times do |k|
      dp[i][(c.to_i * mul + k) % N] += dp[i + 1][k]
    end
  end

  mul *= 10
end

puts dp[0][5] % mod