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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
    implicit none
    integer i, j, k
    integer n_len, tg, pop
    integer :: mod_ = 10**9+7
    integer, allocatable :: dp(:),old_dp(:)
    character(10**5):: S

    read*, S
    n_len = len_trim(S)
    allocate(dp(0:12), old_dp(0:12))
    dp(0:12) = 0
    dp(0) = 1
    old_dp(0:12) = 0
    
    do i=1, n_len
        old_dp(0:12) = dp(0:12)
        dp(0:12) = 0

        if(S(i:i) == "?")then
            do j = 0,9
                do k=0,12
                    pop = mod(k*10+j,13)
                    dp(pop) = dp(pop) + old_dp(k)
                    dp(pop) = mod(dp(pop),mod_)
                enddo
            enddo

        else
            read(S(i:i),*) tg
            do k=0,12
                pop = mod(k*10+tg,13)
                dp(pop) = dp(pop) + old_dp(k)
                dp(pop) = mod(dp(pop),mod_)
            enddo
        endif

    enddo

print'(i0)', dp(5)

stop
end program main