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)

str = gets.chomp
len = str.length

str = str.reverse

dp = Array.new(len + 1).map{Array.new(13, 0)}

if str[0] == '?'
  for i in 0..9
    dp[1][i.to_i.modulo(13)] = 1
  end
else
  dp[1][str[0].to_i.modulo(13)] = 1
end

for n in 1..(len-1)
  if str[n] == '?'
	for i in 0..9
      for j in 0..12
	    dp[n+1][(j + (i * (10 ** n)).modulo(13)).modulo(13)] += dp[n][j]
      end
    end
  else
    for j in 0..12
      dp[n+1][(j + (str[n].to_i * (10 ** n)).modulo(13)).modulo(13)] += dp[n][j]
    end  
  end
end


puts dp[len][5] % (1000_000_007)