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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int S(int num);

int main() {
	int i=0;
	int countM;
	long long j,m;
	int K;
	int n;
	scanf("%lld", &K);
	if(K<=9) {
		for(n = 1;n<=K;n++) {
			printf("%d\n", n);
			i++;
		}
	} else {
		for(n = 1;n<=9;n++) {
			printf("%d\n", n);
			i++;
		}
	}
	for(j = 1;;j++) {
		int success = 1;
		for(countM = 1;countM<10000;countM++) {
			m = j + countM;
			if(m/S(m) <= j/S(j)) {
				success = 0;
			}
		}
		if(success==1) {
			if(i<K) {
				i++;
				printf("%lld\n", j);
			} else {
				break;
			}
		}
	}
    return 0;
}

int S(int y) {
	int result = 0, x;
	while (y != 0) {
        x = y % 10;
        result += x;
        y = (int)(y / 10);
    }
	return result;
}