**6 人解决**，9 人已尝试。

**8 份提交通过**，共有 22 份提交。

**7.0** EMB 奖励。

**单点时限: **2.0 sec

**内存限制: **256 MB

We say that a sequence of integers is a one-sequence if the difference between any two consecutive numbers in this sequence is $1$ or $-1$ and its first element is $0$. More precisely: $[a_1,a_2,\ldots,a_n]$ is a one-sequence if

- for any $k$, such that $1 \le k< n$: $|a_k-a_{k+1}| =1$ and
- $a_1=0$

Write a program that:

- reads two integers describing the length of the sequence and the sum of its elements;
- finds a one-sequence of the given length whose elements sum up to the given value or
- states that such a sequence does not exist.

The number of test cases $t$ is in the first line of input, then $t$ test cases follow separated by an empty line.

In the first line of a test case there is a number $n$, such that $1 \le n \le 10~000$, which is the number of elements in the sequence. In the second line there is a number $S$, which is the sum of the elements of the sequence, such that $|S| \le 50~000~000$.

For each test case there should be written $n$ integers (each integer in a separate line) that are the elements of the sequence ($k$-th element in the $k$-th line) whose sum is $S$ or the word `No`

if such a sequence does not exist. If there is more than one solution your program should output any one.

Consequent test cases should by separated by an empty line.

Input

1 8 4

Output

0 1 2 1 0 -1 0 1

**6 人解决**，9 人已尝试。

**8 份提交通过**，共有 22 份提交。

**7.0** EMB 奖励。

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