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 LuaJIT (2.0.4) (judge verdict: Wrong Answer)

function snuke(k)
  local snuke = 0
  local tmp = k
  while(0 < tmp) do
    local a = tmp % 10
    snuke = snuke + a
    tmp = (tmp - a) / 10
  end
  return k / snuke
end

k = io.read("*n")
dig = 1
cnt = 0
min = 1
res = {}
while(cnt < k) do
  if(dig == 1) then
    for i = 1, 9 do
      cnt = cnt + 1
      print(i)
      table.insert(res, {i, 1})
      if(cnt == k) then break end
    end
  elseif(dig <= 3) then
    -- candidate: 19,29,...,99, 199,299, ..., 999
    base = 0
    mul = 1
    for i = 2, dig do
      base = base * 10 + 9
      mul = mul * 10
    end
    for i = 1, 9 do
      v = base + mul * i
      snk = snuke(v)
      if(min <= snk) then
        cnt = cnt + 1
        min = snk
        print(v)
        table.insert(res, {v, snk})
        if(cnt == k) then break end
      end
    end
  elseif(dig <= 14) then
    -- candidate: 1z9..9, 2z9..9, ..., 9z9..9 z=[0-9]
    base = 0
    mul = 1
    for i = 3, dig do
      base = base * 10 + 9
      mul = mul * 10
    end
    for i = 10, 99 do
      v = base + mul * i
      snk = snuke(v)
      if(min <= snk) then
        cnt = cnt + 1
        min = snk
        print(v)
        table.insert(res, {v, snk})
        if(cnt == k) then break end
      end
    end
  else
    -- candidate: 1xy9..9, 2xy9..9, ..., 9xy9..9 x,y=[0-9]
    base = 0
    mul = 1
    for i = 4, dig do
      base = base * 10 + 9
      mul = mul * 10
    end
    for i = 100, 999 do
      v = base + mul * i
      snk = snuke(v)
      if(min <= snk) then
        cnt = cnt + 1
        min = snk
        print(v)
        table.insert(res, {v, snk})
        if(cnt == k) then break end
      end
    end
  end
  dig = dig + 1
  if(dig == 16) then break end
end