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: Accepted)

# frozen_string_literal: true

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

if k == n
  puts ([s] * n).join(' ')
  exit
end

if s == 1
  a = [s] * k + [1000000000] * (n - k)
  puts a.join(' ')
  exit
end
p = s / 2
q = s - p

a = [p]

1.upto(k) do |i|
  if i.odd?
    a.push q
  else
    a.push p
  end
end

max = 1000000000

max = 1 if s == max

(n - k - 1).times do
  a.push max
end

puts a.join(' ')