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)

K = int(input())
i=1
addNum = 1
ans = []
while(K!=0):
        print(i)
        K-=1
        S1 = 0
        S2 = 0
        for j in list(str(i+addNum)):
                S1 += int(j)
        for j in list(str(i+addNum+addNum)):
                S2 += int(j)
        if (i+addNum)/S1 > (i+addNum+addNum)/S2:
                addNum *= 10
        i += addNum