Problem:
Score : 500 points

Problem Statement

Let S(n) denote the sum of the digits in the decimal notation of n.
For example, S(123) = 1 + 2 + 3 = 6.

We will call an integer n a Snuke number when, for all positive integers m such that m > n, \frac{n}{S(n)} \leq \frac{m}{S(m)} holds.

Given an integer K, list the K smallest Snuke numbers.

Constraints

1 \leq K

The K-th smallest Snuke number is not greater than 10^{15}.

Input

Input is given from Standard Input in the following format:

K

Output

Print K lines. The i-th line should contain the i-th smallest Snuke number.

Sample Input 1

10

Sample Output 1

1
2
3
4
5
6
7
8
9
19

Solution in Kotlin (1.3.71) (judge verdict: Accepted)

import kotlin.math.log10
import kotlin.math.pow

fun main() {
    val k = nextInt()
    var count = 0
    var v = 1L
    do {
        println(v)
        v = sunuke(v + 1)
        count ++
    } while (count < k)
}

fun sunuke(n: Long): Long {
    fun calc(num: Long): Double{
        var sum = 0L
        var m = num
        while (m > 0) {
            sum += m % 10
            m /= 10
        }
        return num.toDouble() / sum
    }

    var sunuke = n
    var minVal = calc(n)

    repeat(log10(n.plus(1).toDouble()).toInt() + 1) {
        val d10 = 10.toDouble().pow(it + 1).toLong()
        val x = d10.times(n.toDouble().div(d10).plus(1).toLong()).minus(1)
        val xVal = calc(x)
        if (minVal > xVal) {
            sunuke = x
            minVal = xVal
        }
    }
    return sunuke
}

// # Utils
// ## Input
fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextList() = next().split(" ")
fun nextIntList() = next().split(" ").map(String::toInt)
fun nextLongList() = next().split(" ").map(String::toLong)
fun nextDoubleList() = next().split(" ").map(String::toDouble)

// ## Array
inline fun <reified T> sizedArray(size: Int, default: T) = Array(size) { default }
inline fun <reified T> sized2DArray(row: Int, column: Int, default: T) = Array(row) { Array(column) { default } }

// ## mod^-1
//    [NOTE] CANNOT use this for 0, mod, 2mod, 3mod ...(return wrong value)
fun modinv(num: Long, mod: Long): Long {
    var a = num
    var b = mod
    var u = 1L
    var v = 0L
    while (b > 0) {
        val t = a.div(b)
        a -= t * b
        a = b.also { b = a } // swap a and b
        u -= t * v
        u = v.also { v = u } // swap u and v
    }
    u %= mod
    if (u < 0) u += mod
    return u
}

fun gcd(x: Int, y: Int): Int {
    fun innerGcd(x: Int, y: Int): Int {
        return if (x % y == 0) y else innerGcd(y, x % y)
    }
    return if (x >= y) innerGcd(x, y) else innerGcd(y, x)
}

fun gcd(x: Long, y: Long): Long {
    fun innerGcd(x: Long, y: Long): Long {
        return if (x % y == 0L) y else innerGcd(y, x % y)
    }
    return if (x >= y) innerGcd(x, y) else innerGcd(y, x)
}

// classes
class UnionFindTree(val size: Int) {
    private val r = sizedArray(size, -1)
    fun root(x: Int): Int {
        if (r[x] < 0) return x
        return root(r[x])
    }

    fun unite(x: Int, y: Int) {
        var rx = root(x)
        var ry = root(y)
        if (rx == ry) return
        if (r[rx] > r[ry]) {
            rx = ry.also { ry = rx }
        }
        r[rx] += r[ry]
        r[ry] = rx
    }

    fun size(x: Int) = -r[root(x)]

    override fun toString(): String {
        return r.joinToString(separator = ", ")
    }
}