An Animal Contest 1 P3 - Happy Alpacas - DMOJ: Modern Online Judge

An Animal Contest 1 P3 - Happy Alpacas

Points: 7 (partial)

Time limit: 2.0s

Memory limit: 256M

Author:

Problem types

Night has fallen, and $N$ ~N~ alpacas have gathered around a campfire. They sit in a circle, that is, alpaca $1$ ~1~ is to the right of alpaca $N$ ~N~, alpaca $2$ ~2~ is to the right of alpaca $1$ ~1~, alpaca $3$ ~3~ is to the right of alpaca $2$ ~2~, and so on. Each alpaca is waiting to be assigned a happiness index, $h_i$ ~h_i~. The $i^\text{th}$ ~i^\text{th}~ alpaca is happy if the sum of its happiness index and the happiness index of the alpaca to its right is even. Otherwise, it is sad. Being a diligent herdsman, you decide to assign each of the $N$ ~N~ alpacas a happiness index such that there are exactly $X$ ~X~ happy alpacas.

Constraints

$2 \le N \le 10^6$ ~2 \le N \le 10^6~

$0 \le X \le N$ ~0 \le X \le N~

Subtask 1 [15%]

$2 \le N \le 15$ ~2 \le N \le 15~

Subtask 2 [85%]

No additional constraints.

Input Specification

The first line contains two space-separated integers, $N$ ~N~ and $X$ ~X~.

Output Specification

If no solution exists, output $-1$ ~-1~. Otherwise, output $N$ ~N~ space-separated integers, the happiness index $h_i$ ~h_i~ for the $i^{th}$ ~i^{th}~ alpaca $(0 \le h_i \le 10^9)$ ~(0 \le h_i \le 10^9)~. If there are multiple solutions, output any.

Note: Output must end with a newline with no trailing whitespace.

Sample Input 1

6 4

Sample Output 1

7 27 196 50 3 17

Explanation for Sample Output 1

The happy alpacas in this arrangement are alpaca $1$ ~1~, alpaca $3$ ~3~, alpaca $5$ ~5~, and alpaca $6$ ~6~. Note that this is not the only solution.

Sample Input 2

2 1

Sample Output 2

-1

Comments

1

nonono commented on June 30, 2025, 9:25 p.m.

that's so cruel, why would you want some alpacas to be sad? T_T

2
pargatsingh commented on March 20, 2025, 4:31 a.m.
Hint

The happiness index doesn't have to be unique per alpaca so feel free to reuse values for simplicity

Try drawing out a few examples with odd/even N with odd/even X and see what pattern you notice.

4

PenguinPush commented on April 26, 2024, 5:18 p.m.

i love an animal contest