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: Accepted)

import scala.io.StdIn._
object Main extends App {
  val Mod = 1000000007
  val s = readLine

  def dp(rems: Array[Long], digit: Char): Array[Long] = {
    val ret = new Array[Long](13)
    val is = if (digit == '?') (0 to 9) else Seq((digit - '0').toInt)
    for {
      i <- is
      j <- (0 to 12)
    } {
      ret((j * 10 + i) % 13) += rems(j)
      ret((j * 10 + i) % 13) %= Mod
    }
    ret
  }

  val init = s.head match {
    case '?' => Array.tabulate(13)(i => if (i < 10) 1L else 0L)
    case c => Array.tabulate(13)(i => if (i == c - '0') 1L else 0L)
  }

  val result = s.tail.foldLeft(init){(z, d) => dp(z, d)}
  println(result(5))
}