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 Ruby (2.3.3) (judge verdict: Wrong Answer)

K = gets.to_i

def digitsum(num)
    ret = 0
    while num > 0
        ret += num % 10
        num /= 10
    end
    ret
end

last = 19
ans = [1, 2, 3, 4, 5, 6, 7, 8, 9, 19]
while ans.length < K
    base = 1
    tmp = last
    while true
        if tmp % 10 == 9
            base *= 10
            tmp /= 10
        else
            num1 = last + base/10
            num2 = last + base
            break
        end
    end
    val1 = num1.to_f / digitsum(num1)
    val2 = num2.to_f / digitsum(num2)
    nextnum = val1 <= val2 ? num1 : num2
    ans.push(nextnum)
    last = nextnum
end
puts ans