Contest Duration: - (local time) (120 minutes) Back to Home
D - Non Arithmetic Progression Set /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• S の要素数は N
• S の要素は -10^7 以上 10^7 以下の相異なる整数
• \displaystyle \sum _{s \in S} s = M
• S の任意の相異なる要素 x,y,z (x < y < z) について y-x\neq z-y

### 制約

• 1 \leq N \leq 10^4
• |M| \leq N\times 10^6
• 入力は全て整数

### 入力

N M


### 出力

S の要素を s_1,s_2,\ldots,s_N とする。条件を満たす S1 つ以下の形式で出力せよ。

s_1 s_2 \ldots s_N


### 入力例 1

3 9


### 出力例 1

1 2 6


2-1 \neq 6-2 であり、 1+2+6=9 なのでこの出力は条件を満たします。他にも様々な答えが考えられます。

### 入力例 2

5 -15


### 出力例 2

-15 -5 0 2 3


M が負のこともあります。

Score : 700 points

### 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.