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: Accepted)

#include <stdio.h>
#include <stdlib.h>
#define int long long

int S(int a){
	int ans = 0;
	while(a > 0){
		ans += a % 10;
		a /= 10;
	}
	return ans;
}

int min(int a, int b){
	if(a * S(b) <= b * S(a)){
		return a;
	}
	else{
		return b;
	}
}

int f(int N){
	int i, j, d, lO, ans = N;
	for(i = 0, lO = 1; i < 16; i++, lO *= 10){
		d = (N / lO) % 10;
		for(j = 1; d + j <= 10; j++){
			ans = min(ans, ((N / lO) + j) * lO - 1);
		}
	}
	return ans;
}

signed main(){
	int K, N = 1, i;
	scanf("%lld", &K);
	for(i = 0; i < K; i++){
		printf("%lld\n", N);
		N = f(N + 1);
	}
	return 0;
}