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: Wrong Answer)

k = int(input())
r = 0  # 桁数
snuke_list = []

def snuke(num):
    s = 0
    for i in str(num):
        s += int(i)
    return num/s

def snuke_check(num):
    n = str(num)
    keta = len(n)    # numの桁数
    min_snuke = int(n[0] + '9'*(keta-1))
    if snuke(num) <= snuke(min_snuke):
        return True
    else:
        return False

count = 0
while count < 2*k:
    for t in range(1, 150):
        num = int(str(t) + '9' * r)
        if snuke_check(num) is True:
            if num not in snuke_list:
                snuke_list.append(num)
                count += 1
        if count >= 2*k:
            break
    r += 1
snuke_list.sort()
check = []
for n in snuke_list:
    check.append(snuke(n))
for i in range(len(check)):
    if check[i] <= min(check[i:]):
        pass
    else:
        snuke_list[i] = -1

for i in range(k):
    if snuke_list[i] > 0:
        print(snuke_list[i])