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 Perl (v5.18.2) (judge verdict: Wrong Answer)

use v5.18; # strict say state
use warnings;
use List::Util qw(reduce first max min sum0);

chomp (my ($n, $k, $s) = split / /, <STDIN>);
my ($x, $y);
if ($s == 1) {
  $x = 2;
  $y = 1e9;
} elsif ($s == 1e9) {
  $x = 1e9;
  $y = 1;
} else {
  $x = $s;
  $y = $s + 1
}
my @c;
for my $i (1..$n) {
  push @c, $x if $i <= $k;
  push @c, $y unless $i <= $k;
}
say join(' ', @c);