311257: CF1957B. A BIT of a Construction

B. A BIT of a Constructiontime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output

Given integers $n$ and $k$, construct a sequence of $n$ non-negative (i.e. $\geq 0$) integers $a_1, a_2, \ldots, a_n$ such that

1. $\sum\limits_{i = 1}^n a_i = k$
2. The number of $1$s in the binary representation of $a_1 | a_2 | \ldots | a_n$ is maximized, where $|$ denotes the bitwise OR operation.

Input

The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.

The only line of each test case contains two integers $n$ and $k$ ($1 \leq n \leq 2 \cdot 10^5$, $1 \leq k \leq 10^9$) — the number of non-negative integers to be printed and the sum respectively.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each test case, output a sequence $a_1, a_2, \ldots, a_n$ on a new line that satisfies the conditions given above.

If there are multiple solutions, print any of them.

ExampleInput

4
1 5
2 3
2 5
6 51

Output

5
1 2
5 0
3 1 1 32 2 12

Note

In the first test case, we have to print exactly one integer, hence we can only output $5$ as the answer.

In the second test case, we output $1, 2$ which sum up to $3$, and $1 | 2 = (11)_2$ has two $1$s in its binary representation, which is the maximum we can achieve in these constraints.

In the fourth test case, we output $3, 1, 1, 32, 2, 12$ which sum up to $51$, and $3 | 1 | 1 | 32 | 2 | 12 = (101\,111)_2$ has five $1$s in its binary representation, which is the maximum we can achieve in these constraints.

题目大意：
给定整数n和k，构造一个由n个非负整数组成的序列a_1, a_2, ..., a_n，使得：

1. a_1 + a_2 + ... + a_n = k
2. 在a_1 | a_2 | ... | a_n的二进制表示中1的数量最大化，其中"|"表示按位或操作。

输入数据格式：
第一行包含一个整数t（1 ≤ t ≤ 10^4）——测试用例的数量。
每个测试用例仅包含一行，有两个整数n和k（1 ≤ n ≤ 2 * 10^5，1 ≤ k ≤ 10^9）——要打印的非负整数的数量和它们的和。
保证所有测试用例的n之和不超过2 * 10^5。

输出数据格式：
对于每个测试用例，输出一个满足上述条件的新行上的序列a_1, a_2, ..., a_n。
如果有多个解，打印其中任何一个。题目大意： 给定整数n和k，构造一个由n个非负整数组成的序列a_1, a_2, ..., a_n，使得： 1. a_1 + a_2 + ... + a_n = k 2. 在a_1 | a_2 | ... | a_n的二进制表示中1的数量最大化，其中"|"表示按位或操作。 输入数据格式： 第一行包含一个整数t（1 ≤ t ≤ 10^4）——测试用例的数量。 每个测试用例仅包含一行，有两个整数n和k（1 ≤ n ≤ 2 * 10^5，1 ≤ k ≤ 10^9）——要打印的非负整数的数量和它们的和。 保证所有测试用例的n之和不超过2 * 10^5。 输出数据格式： 对于每个测试用例，输出一个满足上述条件的新行上的序列a_1, a_2, ..., a_n。 如果有多个解，打印其中任何一个。