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: Wrong Answer)

S = gets.chomp
MOD = 10 ** 9 + 7

dp = Array.new(S.size + 1) { Array.new(13, 0) }
base = 1

if S[-1] == '?'
  10.times do |i|
    dp[1][i] = 1
  end
else
  dp[1][S[-1].to_i] = 1
end

S.chars[1..-1].reverse_each.with_index(1) do |s, idx|
  n = s.to_i

  if s == '?'
    13.times do |i|
      10.times do |j|
        k = (i + (j * base) % 13) % 13
        dp[idx + 1][k] = (dp[idx + 1][k] + dp[idx][i]) % MOD
      end
    end
  else
    13.times do |i|
      j = (i + (n * base) % 13) % 13 
      dp[idx + 1][j] = (dp[idx + 1][j] + dp[idx][i]) % MOD
    end
  end

  base = (base * 10) % 13 
end

puts dp[S.size][5]