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)

# D
K = int(input())
a = 1
b = 0
res_max = 0

while K > 0:
    res = int(str(a) + str(9)*b)
    if res > res_max:
        res_max = res
        print(int(res))
        K -= 1
    if b <= 1:
        if a < 9:
            a += 1
        else:
            a = 1
            b += 1
    elif b == 2:
        if a < int(int(str(9)*max(b, 1))/5):
            a += 1
        else:
            a = 2
            b += 1
    elif b == 3:
        if a < int(str(9)*max(b, 1)):
            a += 1
        else:
            a = 10
            b += 2
    else:
        if a < int(str(9)*max(b, 1)):
            a += 1
        else:
            a = 10
            b += 2