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
S.reverse!
dp = Array.new(S.size+1).map{Array.new(13,0)}
dp[0][0] = 1
digit = 1
mm = 10**9 + 7
(S.size).times{|i|
    if S[i] != '?'
        c = S[i].to_i
        for j in 0..12 do
            dp[i+1][((c * digit) % 13 + j)% 13] += dp[i][j]
            dp[i+1][((c * digit) % 13 + j)% 13] %= mm
        end
    else
        for c in 0..9 do
            for j in 0..12 do
                dp[i+1][((c * digit) % 13 + j)% 13] += dp[i][j]
                dp[i+1][((c * digit) % 13 + j)% 13] %= mm
            end
        end
    end
    digit *= 10
    digit %= 13
}
puts dp[S.size][5]