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:

$A_1$ $A_2$ $...$ $A_N$

4 2 3

1 2 3 4

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

5 3 100

50 50 50 30 70