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 {
  def main(args:Array[String]) = {
    val sc = new java.util.Scanner(System.in)
    val s = sc.next
    var dp = new Array[Int](13)
    var dpn = new Array[Int](13)

    // 初期化(最初は余りは「0」)
    dp(0) = 1

    for (c <- s.toCharArray) {
      dpn = new Array[Int](13)
      // 桁上げ処理
      for (i <- 0 to 12) {
        dpn((i*10)%13) = dp(i)
      }
      dp = dpn
      dpn = new Array[Int](13)

      // 固定値なら値に応じてシフト
      if (c != '?') {
        val v = c.asDigit
        for (i <- 0 to 12) {
          dpn((i+v)%13) += dp(i)
        }
      }
      // ?なら値を0-9とみなしてそれぞれシフト
      else {
        for (v <- 0 to 9) {
          for (i <- 0 to 12) {
            dpn((i+v)%13) += dp(i)
            dpn((i+v)%13) %= 1000000007
          }
        }
      }
      dp = dpn
    }
    println(dp(5))
    //println(dp.deep)
  }
}