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.

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.

Constraints

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

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.

见题面 Input 部分

见题面 Output 部分