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)

val M = 1000000007L

fun co(n: Long): Co {
    return Co((n % M + M) % M)
}

fun main(args: Array<String>) {
    val s = readLine()!!
    val dp = Array(s.length + 1) {Array(13){co(0)}}
    dp[0][0] = co(1)
    for (i in 0 until s.length) {
        if (s[i] == '?') {
            for (j in 0 until 13) {
                for (d in 0 until 10) {
                    dp[i+1][(j * 10 + d) % 13] += dp[i][j]
                }
            }
        } else {
            val c = Character.getNumericValue(s[i])
            for (j in 0 until 13) {
                dp[i+1][(j * 10 + c) % 13] += dp[i][j]
            }
        }
    }
    println(dp[s.length][5].n)
}

data class Co(val n: Long) {
    inline operator fun plus(other: Co): Co {
        return co(n + other.n)
    }
    operator fun minus(other: Co): Co {
        return co(n - other.n)
    }
    operator fun times(other: Co): Co {
        return co(n * other.n)
    }
    operator fun div(other: Co): Co {
        return this * other.pow(M - 2)
    }
    fun pow(k_: Long): Co {
        var k = k_
        var a = this
        var res = co(1)
        while (k > 0) {
            if (k.and(1) == 1L) {
                res *= a
            }
            a *= a
            k = k.shr(1)
        }
        return res
    }
}