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: Accepted)

S = gets.chomp
S.reverse!
size = S.size
a = Array.new(13){Array.new(2,0)}
a[0][0] = 1
b = Array.new(6)
b = [1,10,9,12,3,4]
c = 0
d = 0
h,i,j,k = 0,0,0,0
while h < size
    i = h%6
    if S[h] == "?"
        j = 0
        d = 0
        while j < 13
            d += a[j][i%2]
            j += 1
        end
        j = 0
        while j < 13
            a[j][(i+1)%2] = d
            k = 10
            while k < 13
                a[j][(i+1)%2] -= a[(j-k*b[i%6])%13][i%2]
                k += 1
            end
            a[j][(i+1)%2] %= 10**9+7
            j += 1
        end
    else
        c = S[h].to_i
        j = 0
        while j < 13
            a[(j+c*b[i%6])%13][(i+1)%2] = a[j][i%2]
            j += 1
        end
    end
    h += 1
end
puts a[5][size%2]