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: Accepted)

import math
K = int(input())

def S_n(i):
    return sum(list(map(int, str(i))))

def snuke(n):
    return n / S_n(n)

j = 1
order = 1
for i in range(K):
    print(j)
    if snuke(j + 10**(order-1)) > snuke(j + 10**order):
        order += 1
    j += 10**(order-1)