Problem:
Score : 400 points

Problem Statement

Given are three integers N, K, and S.

Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below.
We can prove that, under the conditions in Constraints, such a sequence always exists.

There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.

Constraints

1 \leq N \leq 10^5

0 \leq K \leq N

1 \leq S \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K S

Output

Print a sequence satisfying the condition, in the following format:

A_1 A_2 ... A_N

Sample Input 1

4 2 3

Sample Output 1

1 2 3 4

Two pairs (l, r) = (1, 2) and (3, 3) satisfy the condition in the statement.

Sample Input 2

5 3 100

Sample Output 2

50 50 50 30 70

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

n, k, s = gets.split.map(&:to_i)
result = []

if s.even?
  if k > 1
    (k + 1).times do
      result << s / 2
    end

    (n - (k + 1)).times do
      result << s + 1 if s < 10**9
      result << s - 1 if s == 10**9
    end
  elsif k == 1
    result << s
  else
    n.times do
      result << s + 1 if s < 10**9
      result << s - 1 if s == 10**9
    end
  end
end

if s.odd?
  if k > 1
    flag = false
    (k + 1).times do
      tmp = flag ? s / 2 : s / 2 + 1
      result << tmp
      flag = !flag
    end

    (n - (k + 1)).times do
      result << s + 1 if s < 10**9
      result << s - 1 if s == 10**9
    end
  elsif k == 1
    result << s
  else
    n.times do
      result << s + 1 if s < 10**9
      result << s - 1 if s == 10**9
    end
  end
end

puts result.join(' ')