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.lang.Math.*

const val MOD = 1000000007L

fun main(args: Array<String>) {
    val s = readList().first()
    val dp = Array<Array<Long>>(1000000) {
        Array(13) {
            return@Array 0L
        }
    }

    dp[0][0] = 1
    s.length.rep { i ->
        var c = -1
        if (s[i] != '?') {
            c = s[i] - '0'
        }

        if (c == -1) {
            10.rep { j ->
                13.rep { k ->
                    dp[i + 1][(k * 10 + j) % 13] += dp[i][k] % MOD
                }
            }

        } else {
            13.rep { k ->
                dp[i + 1][(k * 10 + c) % 13] += dp[i][k] % MOD
            }
        }
        13.rep { k ->
            dp[i + 1][k] %= MOD
        }
    }

    println(dp[s.length][5])
}

fun readList() = readLine()!!.split(' ')
fun readInt() = readLine()!!.split(' ').map(String::toInt).first()
fun readIntList() = readList().map(String::toInt)
fun readLongList() = readList().map(String::toLong)
fun readDoubleList() = readList().map(String::toDouble)

fun readPair(): Pair<String, String> {
    val splite = readLine()!!.split(' ')
    return Pair(splite[0], splite[1])
}

fun <T> List<T>.copy() = this.map { it }

// 速度のためforEachは避ける
inline fun Int.rep(start: Int = 0, body: (Int) -> Unit) {
    for (i in start until this + start) {
        body(i)
    }
}

inline fun Long.rep(start: Long = 0, body: (Long) -> Unit) {
    for (i in start until this + start) {
        body(i)
    }
}

// 約数のList
fun divisor(value: Long): List<Long> {
    val max = sqrt(value.toDouble()).toLong()
    return (1..max)
        .filter { value % it == 0L }
        .map { listOf(it, value / it) }
        .flatten()
        .sorted()
}

// 範囲内の素数を取得
// fromだけ指定すると戻り値の個数で素数判定ができる
fun prime(from: Long, to: Long = from): List<Long> {
    return (from..to).filter { i ->
        val max = Math.sqrt(i.toDouble()).toLong()
        (2..max).all { j -> i % j != 0L }
    }
}

// 素因数分解
fun decom(value: Long): List<Long> {
    if (value == 1L) return listOf(1)
    val max = Math.sqrt(value.toDouble()).toLong()
    return prime(2, max).filter { value % it == 0L }
}

// 最大公約数
fun gcd(a: Long, b: Long): Long {
    return if (a % b == 0L) b else gcd(b, a % b)
}

// 文字列を入れ替え
fun swap(base: String, a: String, b: String): String {
    return base.map {
        when (it) {
            a.toCharArray()[0] -> b
            b.toCharArray()[0] -> a
            else -> it.toString()
        }
    }.joinToString()
}