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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

q=[]
vis=set() 
q=[i for i in range(1,10)]
nums=[]
while q:
   # nums.append(t)
    t=q.pop(0)
    nums.append(t)
    if not t*10+9 in vis  and t*10+9<=10**15:
        q.append(t*10+9)
        vis.add(t*10+9)
nums.sort()
k=int(input())
for i in range(k):
    print(nums[i])