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>

double wari(int x){
	int S=0;
	int j,n=x,m;
	while(n > 9){
		m = n/10;
		j = n-m*10;
		S += j;
		n = m;
	}
	S += n;
	return (double)x/S;
}

int main(void){
	int K;
	scanf("%d",&K);
	int i,c=0,j,flag,x;
	for(i=1;c<K;i++){
		j=1;flag=0;
		int k=wari(i);
		if(x==1){
			if(wari(i-1) <= wari(i)){
				flag=1;
			}
			}else{
			while(j<i){
				if(k >wari(j)){flag=1;x=1;break;}
				j++;
			}
		}
		if(flag==0){
			printf("%d\n",i);
			c++;
		}
		x=0;
	}
	
	
	return 0;
}