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

def digits_parade(s)
  dp = Array.new(13) { 0 }
  dp[0] = 1

  mul = 1
  s.reverse.each_char do |c|
    nextDp = Array.new(13) { 0 }
    if c == '?'
      0.upto(9) do |n|
        r = (n * mul) % 13
        0.upto(12) do |i|
          nextDp[(r + i) % 13] += dp[i]
        end
      end
    else
      r = (c.to_i * mul) % 13
      0.upto(12) do |i|
        nextDp[(r + i) % 13] += dp[i]
      end
    end
    mul *= 10
    dp = nextDp
  end

  dp[5] % MOD
end

puts digits_parade(gets.chomp)