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)

character(10**5) S
integer,allocatable,dimension(:,:)::DP
integer keta(6)
integer SL
read*,S
SL=len_trim(S)
allocate(DP(0:12,SL))
DP=0
keta=[1,10,9,12,3,4]

if(S(SL:SL)=="?")then
  do i=0,9
    DP(i,1)=1
  end do
else 
  DP(ichar(S(SL:SL))-48,1)=1
end if

do i=2,SL
  if(S(SL-i+1:SL-i+1)=="?")then
  do j=0,9
    do k=0,12
      jj=mod(j*Keta( mod(i-1,6) +1 )+k,13)
      DP(jj,i)=mod(DP(jj,i)+DP(k,i-1),10**9+7)
    end do
  end do
  else
    jj=(ichar(S(SL-i+1:SL-i+1))-48)*Keta( mod(i-1,6) +1 )
    do j=0,12
      DP(mod(jj+j,13),i)=DP(j,i-1)
    end do
  endif
end do

print"(i0)",DP(5,SL)
end