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 8.8.3) (judge verdict: Accepted)

import Control.Monad
import Data.Maybe
import qualified Data.ByteString.Char8 as BS
import Data.List
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import Data.Char
import Data.Array

main = do
    s <- getLine
    let arr = array ((0,0),(12,9)) [((i,j), (i*10+j) `mod` 13)| i <- [0..12], j <- [0..9]]
    let f v c | c == '?' = VU.create $ do
                                vec <- VUM.replicate 13 (0 :: Int)
                                forM_ [0..12] $ \i -> do
                                    forM_ [0..9] $ \j -> do
                                        let a = v VU.! i
                                        VUM.modify vec (\b -> (a + b) `mod` 1000000007) (arr ! (i,j))
                                return vec
              | otherwise = VU.create $ do
                                vec <- VUM.replicate 13 (0 :: Int)
                                forM_ [0..12] $ \i -> do
                                    VUM.write vec (arr ! (i, digitToInt c)) (v VU.! i)
                                return vec
    let ans = foldl' f (VU.fromList (1 : replicate 12 0)) s
    print $ ans VU.! 5