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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val s = readLine() ?: return
    val mod = 1000000000 + 7
    val n = s.length

    var dp = listOf(1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L)

    for (i in 0 until n) {
        val c = s[i]
        val ndp = mutableListOf(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L)
        if (c != '?') {
            val num = c.toString().toInt()
            for (m in 0 until 13) {
                ndp[(m * 10 + num) % 13] += dp[m]
            }
        } else {
            for (num in 0 until 10) {
                for (m in 0 until 13) {
                    ndp[(m * 10 + num) % 13] += dp[m]
                }
            }
        }
      
        dp = ndp.map { it % mod }
    }

    println(dp[5])
}