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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.List
main=getLine>>=print.e
 where e (c:s) = f (if c=='?' then ((replicate 10 1)++[0,0,0]) else (take 13 ((replicate (read [c]) 0)++(1:(repeat 0))))) s
       f l [] = l!!5
       f l (c:s) = let k=(map (l!!) [0,4,8,12,3,7,11,2,6,10,1,5,9]) in (if c=='?' then (f (g k) s) else (f (h (read [c]) k) s))
       g k = let kk=(reverse (k++k)) in (map (i kk) [12,11..0])
       h c k = ((drop (13-c) k)++(take (13-c) k))
       i k j = mod(sum(take 10 (drop j k)))1000000007