201453: [AtCoder]ARC145 D - Non Arithmetic Progression Set

Problem Statement

Construct a set $S$ of integers satisfying all of the conditions below. It can be proved that at least one such set $S$ exists under the Constraints of this problem.

• $S$ has exactly $N$ elements.
• The element of $S$ are distinct integers between $-10^7$ and $10^7$ (inclusive).
• $ \displaystyle \sum _{s \in S} s = M$.
• $ y-x\neq z-y$ for every triple $ x,y,z$ $(x < y < z)$ of distinct elements in $ S$.

Constraints

• $1 \leq N \leq 10^4$
• $|M| \leq N\times 10^6$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

Output

Let $s_1,s_2,\ldots,s_N$ be the elements of $S$. Print a set $S$ that satisfies the conditions in the following format:

$s_1$ $s_2$ $\ldots$ $s_N$

If multiple solutions exist, any of them will be accepted.

Sample Input 1

3 9

Sample Output 1

1 2 6

We have $2-1 \neq 6-2$ and $1+2+6=9$, so this output satisfies the conditions. Many other solutions exist.

Sample Input 2

5 -15

Sample Output 2

-15 -5 0 2 3

$M$ may be negative.