CF1726B.Mainak and Interesting Sequence

Mainak has two positive integers $n$ and $m$.

Mainak finds a sequence $a_1, a_2, \ldots, a_n$ of $n$ positive integers interesting, if for all integers $i$ ($1 \le i \le n$), the bitwise XOR of all elements in $a$ which are strictly less than $a_i$ is $0$. Formally if $p_i$ is the bitwise XOR of all elements in $a$ which are strictly less than $a_i$, then $a$ is an interesting sequence if $p_1 = p_2 = \ldots = p_n = 0$.

For example, sequences $[1,3,2,3,1,2,3]$, $[4,4,4,4]$, $[25]$ are interesting, whereas $[1,2,3,4]$ ($p_2 = 1 \ne 0$), $[4,1,1,2,4]$ ($p_1 = 1 \oplus 1 \oplus 2 = 2 \ne 0$), $[29,30,30]$ ($p_2 = 29 \ne 0$) aren't interesting.

Here $a \oplus b$ denotes bitwise XOR of integers $a$ and $b$.

Find any interesting sequence $a_1, a_2, \ldots, a_n$ (or report that there exists no such sequence) such that the sum of the elements in the sequence $a$ is equal to $m$, i.e. $a_1 + a_2 \ldots + a_n = m$.

As a reminder, the bitwise XOR of an empty sequence is considered to be $0$.

Mainak 有两个正整数 $n$ 和 $m$。

Mainak 将一个由 $n$ 个正整数组成的序列 $a_1, a_2, \ldots, a_n$ 称为有趣的序列，当且仅当对所有整数 $i$（$1 \le i \le n$），序列 $a$ 中所有严格小于 $a_i$ 的元素的按位异或结果为 $0$。形式化地，若记 $p_i$ 为序列 $a$ 中所有严格小于 $a_i$ 的元素的按位异或值，则当且仅当 $p_1 = p_2 = \ldots = p_n = 0$ 时，序列 $a$ 是有趣的。

例如，序列 $[1,3,2,3,1,2,3]$、$[4,4,4,4]$、$[25]$ 是有趣的；而序列 $[1,2,3,4]$（因为 $p_2 = 1 \ne 0$）、$[4,1,1,2,4]$（因为 $p_1 = 1 \oplus 1 \oplus 2 = 2 \ne 0$）、$[29,30,30]$（因为 $p_2 = 29 \ne 0$）则不是有趣的。

此处 $a \oplus b$ 表示整数 $a$ 与 $b$ 的按位异或。

请构造任意一个有趣的序列 $a_1, a_2, \ldots, a_n$（若不存在则报告无解），使得该序列中所有元素之和等于 $m$，即满足 $a_1 + a_2 + \ldots + a_n = m$。

提醒：空序列的按位异或值定义为 $0$。

Each test contains multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 10^5$) — the number of test cases. Description of the test cases follows.

The first line and the only line of each test case contains two integers $n$ and $m$ ($1 \le n \le 10^5$, $1 \le m \le 10^9$) — the length of the sequence and the sum of the elements.

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

每个测试包含多个测试用例。第一行包含一个整数 $t$（$1 \le t \le 10^5$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例仅有一行，包含两个整数 $n$ 和 $m$（$1 \le n \le 10^5$，$1 \le m \le 10^9$），分别表示序列的长度和元素之和。

保证所有测试用例的 $n$ 之和不超过 $10^5$。

For each test case, if there exists some interesting sequence, output "Yes" on the first line, otherwise output "No". You may print each letter in any case (for example, "YES", "Yes", "yes", "yEs" will all be recognized as positive answer).

If the answer is "Yes", output $n$ positive integers $a_1, a_2, \ldots, a_n$ ($a_i \ge 1$), forming an interesting sequence such that $a_1 + a_2 \ldots + a_n = m$. If there are multiple solutions, output any.

对于每个测试用例，如果存在某个有趣的序列，则在第一行输出“Yes”；否则输出“No”。你可以以任意大小写形式输出每个字母（例如，“YES”、“Yes”、“yes”、“yEs”均会被识别为肯定回答）。

如果答案为“Yes”，则输出 $n$ 个正整数 $a_1, a_2, \ldots, a_n$（满足 $a_i \ge 1$），构成一个有趣的序列，使得 $a_1 + a_2 + \ldots + a_n = m$。若存在多个解，输出任意一个即可。

• In the first test case, $[3]$ is the only interesting sequence of length $1$ having sum $3$.

• In the third test case, there is no sequence of length $2$ having sum of elements equal to $1$, so there is no such interesting sequence.

• In the fourth test case, $p_1 = p_2 = p_3 = 0$, because bitwise XOR of an empty sequence is $0$.

• 在第一个测试用例中，$[3]$ 是唯一一个长度为 $1$ 且元素和为 $3$ 的有趣序列。

• 在第三个测试用例中，不存在长度为 $2$ 且元素和等于 $1$ 的序列，因此不存在这样的有趣序列。

• 在第四个测试用例中，$p_1 = p_2 = p_3 = 0$，因为空序列的按位异或（bitwise XOR）值为 $0$。