Problem:
Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36

Solution in Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.IOException
import java.io.InputStream
import java.util.*

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)
    val k = sc.nextInt()

    val deque = ArrayDeque<Node>()
    deque.add(Node(1, 1))

    val minDistance = IntArray(k) { Int.MAX_VALUE }
    while (deque.isNotEmpty()) {
        val node = deque.poll()
        if (minDistance[node.value] <= node.distance) continue

        minDistance[node.value] = node.distance
        if (node.value == 0) break

        deque.addFirst(Node(node.value * 10 % k, node.distance))
        deque.addLast(Node((node.value + 1) % k, node.distance + 1))
    }

    println(minDistance[0])
}

data class Node(val value: Int, val distance: Int)

class Scanner(private val `in`: InputStream) {
    private val buffer = ByteArray(1024)
    private var ptr = 0
    private var buflen = 0

    companion object {
        private fun isPrintableChar(b: Byte): Boolean = b in 33..126
        private fun isNumericChar(b: Byte): Boolean = b in 48..57
        private fun digit(b: Byte): Int = b - 48
    }

    fun hasNextByte(): Boolean {
        if (ptr < buflen) return true
        ptr = 0
        try {
            buflen = `in`.read(buffer)
        } catch (e: IOException) {
            e.printStackTrace()
        }
        return 0 < buflen
    }

    private fun readByte(): Byte = if (hasNextByte()) buffer[ptr++] else -1

    private fun skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++
    }

    fun hasNext(): Boolean {
        skipUnprintable()
        return hasNextByte()
    }

    fun next(): String {
        if (!hasNext()) throw NoSuchElementException()
        return buildString {
            var b = readByte()
            while (isPrintableChar(b)) {
                appendCodePoint(b.toInt())
                b = readByte()
            }
        }
    }

    fun nextInt(): Int {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0
        var b = readByte()
        val minus = b.toChar() == '-'
        if (minus) b = readByte()
        if (!isNumericChar(b)) throw NumberFormatException()
        do {
            n *= 10
            n += digit(b)
            b = readByte()
        } while (isNumericChar(b))
        return if (minus) -n else n
    }

    fun nextInts(n: Int): Array<Int> = Array(n) { nextInt() }

    fun nextIntArray(n: Int): IntArray = IntArray(n) { nextInt() }

    fun nextIntArrays(n: Int, m: Int): Array<IntArray> {
        val arrays = Array(m) { IntArray(n) }
        repeat(n) { i -> repeat(m) { j -> arrays[j][i] = nextInt() } }
        return arrays
    }

    fun nextLong(): Long {
        if (!hasNext()) throw NoSuchElementException()
        var n = 0L
        var b = readByte()
        val minus = b.toChar() == '-'
        if (minus) b = readByte()
        if (!isNumericChar(b)) throw NumberFormatException()
        do {
            n *= 10
            n += digit(b)
            b = readByte()
        } while (isNumericChar(b))
        return if (minus) -n else n
    }

    fun nextLongs(n: Int): Array<Long> = Array(n) { nextLong() }

    fun nextLongArray(n: Int): LongArray = LongArray(n) { nextLong() }

    fun nextLongArrays(n: Int, m: Int): Array<LongArray> {
        val arrays = Array(m) { LongArray(n) }
        repeat(n) { i -> repeat(m) { j -> arrays[j][i] = nextLong() } }
        return arrays
    }

}