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: Runtime Error)

K = int(input())

snuke = [1,2,3,4,5,6,7,8,9,19,29,39,49,59,69,79,89,99,199,299,399,499,599,699,799,899,999]

for n in range(3,16):
    for k in range(1,11):
        snuke.append(10**(n-1)*(10+k)-1)
    for k in range(2,10):
        snuke.append((k+1)*10**n-1)

for k in range(K):
    print(snuke[k])