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
N = S.size
MOD = 10**9+7

dp = Array.new(N+1){Array.new(13, 0)}
dp[0][0] = 1
N.times do |i|
    if S[i] == '?'
        10.times do |j|
            13.times do |k|
                dp[i+1][(10*k+j)%13] += dp[i][k]
            end
        end
    else
        j = S[i].to_i
        13.times do |k|
            dp[i+1][(10*k+j)%13] += dp[i][k]
        end
    end
    13.times do |k|
        dp[i+1][k] -= MOD while dp[i+1][k] >= MOD
    end
end
puts dp[N][5]