Problem:
Score : 800 points

Problem Statement

In Finite Encyclopedia of Integer Sequences (FEIS), all integer sequences of lengths between 1 and N (inclusive) consisting of integers between 1 and K (inclusive) are listed.

Let the total number of sequences listed in FEIS be X. Among those sequences, find the (X/2)-th (rounded up to the nearest integer) lexicographically smallest one.

Constraints

1 \leq N,K \leq 3 × 10^5

N and K are integers.

Input

Input is given from Standard Input in the following format:

K N

Output

Print the (X/2)-th (rounded up to the nearest integer) lexicographically smallest sequence listed in FEIS, with spaces in between, where X is the total number of sequences listed in FEIS.

Sample Input 1

3 2

Sample Output 1

2 1

There are 12 sequences listed in FEIS: (1),(1,1),(1,2),(1,3),(2),(2,1),(2,2),(2,3),(3),(3,1),(3,2),(3,3).
The (12/2 = 6)-th lexicographically smallest one among them is (2,1).

Sample Input 2

2 4

Sample Output 2

1 2 2 2

Sample Input 3

5 14

Sample Output 3

3 3 3 3 3 3 3 3 3 3 3 3 2 2

Solution in LuaJIT (2.0.4) (judge verdict: Time Limit Exceeded)

local k, n = io.read("*n", "*n")
local t = {}

if k % 2 == 0 then
  table.insert(t, k / 2)
  for i = 1, n - 1 do table.insert(t, k) end
else
  local hk = (k + 1) / 2
  for i = 1, n do t[i] = hk end
  local decnum = math.ceil((n - 1) / 2)
  for i = 1, decnum do
    for j = n, 1, -1 do
      if 0 < t[j] then
        t[j] = t[j] - 1
        if t[j] ~= 0 then
          for s = j + 1, n do
            t[s] = k
          end
        end
        break
      end
    end
  end
  for i = 1, n do
    if t[i] == 0 then
      for j = i, n do
        table.remove(t)
      end
      break
    end
  end
end

print(table.concat(t, " "))