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)

import java.io.*
import java.util.*

const val MOD = 1000000007
fun solve(S: String) {
    val n = S.length
    // dp[mod][i] = 左からi桁まで見て、あまりがmodであるものの数
    val dp = Array(13) { LongArray(n + 1) }
    dp[0][0] = 1L
    for (i in 1..n) {
        for (mod in 0..12) {
            val digits = when (S[i - 1]) {
                '?' -> (0..9).asSequence()
                else -> sequenceOf(S[i - 1] - '0')
            }
            for (digit in digits) {
                val nextMod = (mod * 10 + digit).floorMod(13).toInt()
                dp[nextMod][i] += dp[mod][i - 1]
                dp[nextMod][i] = dp[nextMod][i] % MOD
            }
        }
    }
    // println(dp.contentDeepToString())
    println(dp[5][n])
    return
}

fun Int.floorMod(mod: Int): Int{
    val ret = this % mod
    return if (ret >= 0) ret else ret+mod
}

fun main(args: Array<String>) {
    fun StringArray(size: Int, init: (Int) -> String = { "\u0000" }): Array<String> {
        return Array<String>(size, init)
    }
    class Scanner(stream: InputStream) {
        private val reader = BufferedInputStream(stream).bufferedReader()
        private var st: StringTokenizer? = null
        fun next(): String {
            while (!(st?.hasMoreTokens() ?: false)) st = StringTokenizer(reader.readLine())
            return st!!.nextToken()
        }
    }
    val sc = Scanner(System.`in`)
    val S = sc.next()
    solve(S)
}