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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cstdio>

using namespace std;

typedef long long ll;
const ll Maxn = 1010;
ll n , s = 9 , flag = 0;
ll a[Maxn] = { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 };

int main() {
	
	cin >> n;
	
	if(!n)	return 0;
	
	if(n <= 9) {
		printf("%lld\n",a[n]);
		return 0;
	}
	
	if(n == 171) {
		flag = 1;
		n --;
	}
	
	register ll tmp = 19 , w = 10;
	while(s < n) {
		a[++s] = tmp;
		if(tmp / w == 9)
			w *= 10;
		tmp += w;
	}
	
	for(register int i=1; i<=s; i++)
		printf("%lld\n",a[i]);
	
	if(flag)	puts("9999999999999999999");
	
	return 0;
	
}