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.to_s
@s_array = @s.split('').reverse
@n = @s.length
@dp = []

# @param Int
# @return Array
def remainders_for_question(i)
  output = []
  digit = 10**i
  0.upto(9) do |j|
    remeinder = digit*j%13
    @dp[i - 1].each_with_index do |v, idx|
      k = (remeinder + idx)%13
      next if v.nil?
      if output[k].nil?
        output[k] = v
      else
        output[k] += v
      end
    end if i > 0
    output[remeinder] = 1 if i == 0
  end
  return output
end

# @param Int, Int
# @return Array
def remainders_for_number(i, target)
  output = []
  digit = 10**i
  remeinder = (digit*target)%13
  return output = @dp[i - 1].rotate(13 - remeinder)
end

def first_step(target)
  output = Array.new(13, 0)
  if target == "?"
    0.upto(9) do |i|
      output[i] = 1
    end
  else
    output[target.to_i] = 1
  end
  return output
end

0.upto(@n - 1) do |i|
  target = @s_array[i]
  if i == 0
    @dp[0] = first_step(target)
  elsif target == '?'
    @dp[i] = remainders_for_question(i)
  else
    @dp[i] = remainders_for_number(i, target.to_i)
  end
end

# print @dp
print (@dp[@n - 1][5].to_i)%(10**9+7)