Problem:
Score : 100 points

Problem Statement

Find the number of integers between 1 and K (inclusive) satisfying the following condition, modulo 10^9 + 7:

The sum of the digits in base ten is a multiple of D.

Constraints

All values in input are integers.

1 \leq K < 10^{10000}

1 \leq D \leq 100

Input

Input is given from Standard Input in the following format:

K
D

Output

Print the number of integers satisfying the condition, modulo 10^9 + 7.

Sample Input 1

30
4

Sample Output 1

6

Those six integers are: 4, 8, 13, 17, 22 and 26.

Sample Input 2

1000000009
1

Sample Output 2

2

Be sure to print the number modulo 10^9 + 7.

Sample Input 3

98765432109876543210
58

Sample Output 3

635270834

Solution in Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

fun main(args: Array<String>) = IO().println {
    val K = string()
    val n = K.length
    val D = int()
    val dp = mdArray( co(0), n+1, D, 2)
    dp[0,0,0] = co(1)
    for (i in n) for (j in D) for (less in 2) {
        val c = Character.getNumericValue(K[i])
        for (d in if (less == 0) c+1 else 10)
            dp[i+1, (j + d) % D, less or (if (d < c) 1 else 0)] += dp[i,j,less]
    }
    dp[n,0,0] + dp[n,0,1] - co(1)
}

inline fun <reified T> mdArray(init: T, vararg dims: Int): MdArray<T> {
    return MdArray(dims, Array(dims.fold(1, {acc, x -> acc * x})){init})
}

class MdArray<T>(val dims: IntArray, val arr: Array<T>) {
    inline fun flatten(indices: IntArray): Int {
        return dims.indices.fold(0, {acc, i -> acc + indices[i] * dims.drop(i+1).fold(1,{acc2,x->acc2*x})})
    }
    inline operator fun set(vararg indices: Int, v: T) {
        arr[flatten(indices)] = v
    }
    inline operator fun get(vararg indices: Int): T {
        return arr[flatten(indices)]
    }
}

const val M = 1000000007L

fun co(n: Long) = Co(n % M)

data class Co(val n: Long) {
    override fun toString(): String = n.toString()
    operator fun plus(other: Co): Co {
        return co(n + other.n)
    }
    operator fun minus(other: Co): Co {
        return co((n - other.n) % M + M)
    }
    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
    }
}

// region template
operator fun Int.iterator() = 0.until(this).iterator()

class IO {
    val printable = 33..126
    val buffer = ByteArray(1024)
    var ptr = 0
    var buflen = 0
    val out = java.io.PrintWriter(System.out)
    fun hasNextByte(): Boolean = if (ptr < buflen) true else {
        ptr = 0
        buflen = System.`in`.read(buffer)
        buflen > 0
    }

    fun readByte(): Byte = if (hasNextByte()) buffer[ptr++] else -1
    fun hasNext(): Boolean {
        while (hasNextByte() && buffer[ptr] !in printable) ptr++
        return hasNextByte()
    }

    fun string(): String {
        if (!hasNext()) throw java.util.NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while (b in printable) {
            sb.appendCodePoint(b.toInt())
            b = readByte()
        }
        return sb.toString()
    }

    fun long(): Long {
        if (!hasNext()) throw java.util.NoSuchElementException()
        var n = 0L
        var minus = false
        var b = readByte()
        if (b == '-'.toByte()) {
            minus = true
            b = readByte()
        }
        if (b !in '0'.toByte()..'9'.toByte()) {
            throw NumberFormatException()
        }
        while (true) {
            if (b in '0'.toByte()..'9'.toByte()) {
                n *= 10
                n += b - '0'.toByte()
            } else if (b == (-1).toByte() || b !in printable) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun int(): Int {
        val nl = long()
        if (nl !in Integer.MIN_VALUE..Integer.MAX_VALUE) throw NumberFormatException()
        return nl.toInt()
    }

    fun double(): Double = string().toDouble()
    fun print(obj: Any) = out.print(obj)
    fun print(i: Int) = out.print(i)
    fun print(l: Long) = out.print(l)
    fun println(obj: Any) = out.println(obj)
    fun println(i: Int) = out.println(i)
    fun println(l: Long) = out.println(l)
    inline fun exec(block: IO.() -> Unit) {
        block()
        out.flush()
    }

    inline fun println(block: IO.() -> Any) {
        println(block())
        out.flush()
    }
}
// endregion