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)

K = int(input())

Ans = [1, 2, 3, 4, 5, 6, 7, 8, 9]
for x in range(1,16):
    B = [0]*100000
    n,d = 10**x,int("9"*x)
    for i in range(10000):
        num = i*n+d
        S = str(num)
        total = 0
        for s in S:
            total += int(s)
        B[i] = num/total
        if i > 0:
            if B[i] < B[i-1]:
                #最後の値を削除
                Ans.pop()
                break
            else:
                Ans.append(num)

for i in range(K):
    print(Ans[i])