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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import (
	"fmt"
	"os"
	"strconv"
	"strings"
)

func strintToInt(s string) int {
	i, _ := strconv.Atoi(s)
	return i
}

func calc(n int) float64 {
	sum := 0
	for _, digit := range strings.Split(fmt.Sprintf("%d", n), "") {
		sum += strintToInt(digit)
	}
	return float64(n) / float64(sum)
}

func isSnuk(n int) bool {
	if n < 10 {
		return true
	}
	info := strings.Split(fmt.Sprintf("%d", n), "")
	for i := 1; i < len(info); i++ {
		if info[i] != "9" {
			return false
		}
	}
	return true
}

func main() {
	var K int
	fmt.Scan(&K)
	i := 1
	num := 0
	for {
		if isSnuk(i) {
			fmt.Println(i)
			num += 1
			if num == K {
				os.Exit(0)
			}
		}
		i += 1
	}
}