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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

//package practice.task1

import scala.collection.mutable

object Main extends App {
  val S: String = io.StdIn.readLine()
  val MOD = 1000000007
  var dp: Seq[mutable.HashMap[Int, Long]] =
    (0 to S.length).map(
      _ =>
        mutable.HashMap[Int, Long](
          (0, 0),
          (1, 0),
          (2, 0),
          (3, 0),
          (4, 0),
          (5, 0),
          (6, 0),
          (7, 0),
          (8, 0),
          (9, 0),
          (10, 0),
          (11, 0),
          (12, 0)
      )
    )
  dp.head(0) = 1

  var m: Int = 1
  for (i <- 0 until S.length) {
    val C: Char = S(S.length - i - 1)
    if (C != '?')
      for (k <- 0 to 12) {
        dp(i + 1)((k + m * C.toString.toInt % 13) % 13) = dp(i)(k)
      } else
      for (j <- 0 to 9) {
        for (k <- 0 to 12) {
          val t = (k + m * j % 13) % 13
          dp(i + 1)(t) = (dp(i + 1)(t) + dp(i)(k)) % MOD
        }
      }
    m = m * 10 % 13
  }

  println(dp(S.length)(5))
}