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: Accepted)

def Ask(x):
    ans = 0
    while (x):
        ans += x % 10
        x //= 10
    return ans

def Check(x, y):
    return x * Ask(y) > y * Ask(x)


k = int(input())
no = st = 1
while (k):
    k -= 1
    print(no)
    if (Check(no + st, no + st * 10)): st *= 10
    no += st