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.chomp.split(" ").map(&:to_i)
array = [s]

(1...k).each do
  if array.last.even?
    last = array.last 
    array.push(last / 2)
    array.push(last / 2)
  else
    last = array.last
    array.push(last / 2 + 1)
    array.push(last / 2)
  end
end

a = n - array.length

(1..a).each do
  array.push(s+1)
end

puts array.join(" ")