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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

k = int(input())

import numpy as np

def sunuke(n):
    return n / sum(map(int,list(str(n))))

count_k = 0
for i in range(1,10**15+1):
    d = len(str(i))
    loop_list = np.arange(i,10**(d-1)) * (10 ** (d-1)) + 9
    for j in range(i,10**d):
        if sunuke(i) > sunuke(j):
            break
    else:
        count_k += 1
        print(i)
        if count_k == k:
            break