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)

ns = gets.chomp.split('').map{|m| m == '?' ? '?' : m.to_i}

dp = Array.new(ns.size) { Array.new(13, 0) }

if ns[0] == '?'
  10.times{|t| dp[0][t] = 1 }
else
  dp[0][ns[0]] = 1
end

dp.each_with_index do |d, i|
  next if i == ns.size - 1
  n = ns[i+1]
  d.each_with_index {|b, bi|
    if n == '?'
      10.times {|t|
        ne = (bi * 10 + t) % 13
        dp[i+1][ne] += b
        dp[i+1][ne] %= 1_000_000_007
      }
    else
      ne = (bi * 10 + n) % 13
      dp[i+1][ne] += b
      dp[i+1][ne] %= 1_000_000_007
    end
  }
end

p dp.last[5]