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)


def eval_sn(n):
    s = str(n)
    ans = 0
    for i in s:
        ans += int(i)
    return n/ans

if __name__ == "__main__":
    K = int(input())
    n = 0
    Sn = [0] # 添字0は便宜上埋めておく
    RANGE_ = 50
    while n != RANGE_:
        n += 1
        Sn.append(eval_sn(n))

    while K != 0:
        n += 1
        #
        Sn.append(eval_sn(n))
        check = 0
        for j in range(RANGE_):
            if (Sn[n-RANGE_] <= Sn[n-j]):
                check += 1
                continue
            else:
                break
        if check == RANGE_:
            K -= 1
            print(n-RANGE_)