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)


object Main extends App {
  import scala.io.StdIn._
  val MOD = 1000000007L
  val str = readLine.trim
  var digit = 1
  val count = Array.fill(13){0L}
  count(0) = 1
  for (c <- str.reverse) {
    val temp = Array.fill(13){0L}
    c match {
      case '?' =>
        for (d <- 0 until 10) {
          val diff = d * digit
          for (p <- 0 until 13) {
            temp((p + diff) % 13) += count(p)
          }
        }
      case _ =>
        val diff = c.asDigit * digit
        for (p <- 0 until 13) {
          temp((p + diff) % 13) += count(p)
        }
    }
    for (i <- 0 until 13) {
      count(i) = temp(i) % MOD
    }
    digit = (digit * 10) % 13
  }
  println(count(5))
}