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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <stdint.h>
#include <string.h>
#include <wchar.h>

#define MIN(a, b) (a < b ? a : b)
#define MAX(a, b) (a > b ? a : b)

static uint32_t SN[10];

int main(void) {
	uint64_t K;

	scanf("%"PRIu64, &K);

	uint64_t count = 0;
	while (count < K && count < 9){
		count == K - 1 ? printf("%"PRIu64, (uint64_t)(count + 1)) : printf("%"PRIu64"\n", (uint64_t)(count + 1));

		count++;
	}
	while (count < K) {
		count == K - 1 ? printf("%"PRIu64, (uint64_t)((count - 8) * 10) + 9) : printf("%"PRIu64"\n", (uint64_t)((count - 8) * 10 + 9));

		count++;
	}

	return 0;
}