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)

# N = gets.chomp.to_i
# A = gets.chomp.split.map(&:to_i)

S = gets.chomp.chars
n = S.size
MOD = 10 ** 9 + 7

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

## recurrence relation
# - dp[i + 1][(k * 10 + j) % 13] sum(k 0-12,j 0-9) dp[i][k]
#   - summention of "13 * 10"

dp[0][0] = 1
0.upto(n-1).each do |i|
  '0'.upto('9').each do |c|
    if S[i] != '?' && S[i] != c
      # We ignore this case
      next
    end

    j = c.ord - '0'.ord
    0.upto(12).each do |k|
      dp[i + 1][(k * 10 + j) % 13] += dp[i][k]
    end
  end
    
  0.upto(12).each do |k|
    dp[i + 1][k] %= MOD
  end
end

p dp[n][5]