[Solution] Mainak and Interesting Sequence Codeforces Solution

B. Mainak and Interesting Sequence

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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

Mainak finds a sequence 𝑎1,𝑎2,…,𝑎𝑛$a_1,a_2,\dots ,a_n$ of 𝑛$n$ positive integers interesting, if for all integers 𝑖$i$ (1≤𝑖≤𝑛$1\le i\le n$), the bitwise XOR of all elements in 𝑎$a$ which are strictly less than 𝑎𝑖$a_i$ is 0$0$. Formally if 𝑝𝑖$p_i$ is the bitwise XOR of all elements in 𝑎$a$ which are strictly less than 𝑎𝑖$a_i$, then 𝑎$a$ is an interesting sequence if 𝑝1=𝑝2=…=𝑝𝑛=0$p_1=p_2=\dots =p_n=0$.

For example, sequences [1,3,2,3,1,2,3]$[1,3,2,3,1,2,3]$, [4,4,4,4]$[4,4,4,4]$, [25]$[25]$ are interesting, whereas [1,2,3,4]$[1,2,3,4]$ (𝑝2=1≠0$p_2=1\ne 0$), [4,1,1,2,4]$[4,1,1,2,4]$ (𝑝1=1⊕1⊕2=2≠0$p_1=1\oplus 1\oplus 2=2\ne 0$), [29,30,30]$[29,30,30]$ (𝑝2=29≠0$p_2=29\ne 0$) aren't interesting.

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

Find any interesting sequence 𝑎1,𝑎2,…,𝑎𝑛$a_1,a_2,\dots ,a_n$ (or report that there exists no such sequence) such that the sum of the elements in the sequence 𝑎$a$ is equal to 𝑚$m$, i.e. 𝑎1+𝑎2…+𝑎𝑛=𝑚$a_1+a_2\dots +a_n=m$.

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

Input

Each test contains multiple test cases. The first line contains a single integer 𝑡$t$ (1≤𝑡≤105$1\le t\le {10}^5$) — the number of test cases. Description of the test cases follows.

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The first line and the only line of each test case contains two integers 𝑛$n$ and 𝑚$m$ (1≤𝑛≤105$1\le n\le {10}^5$, 1≤𝑚≤109$1\le m\le {10}^9$) — the length of the sequence and the sum of the elements.

It is guaranteed that the sum of 𝑛$n$ over all test cases does not exceed 105${10}^5$.

Output

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$n$ positive integers 𝑎1,𝑎2,…,𝑎𝑛$a_1,a_2,\dots ,a_n$ (𝑎𝑖≥1$a_i\ge 1$), forming an interesting sequence such that 𝑎1+𝑎2…+𝑎𝑛=𝑚$a_1+a_2\dots +a_n=m$. If there are multiple solutions, output any.

Note

• In the first test case, [3]$[3]$ is the only interesting sequence of length 1$1$ having sum 3$3$.
• In the third test case, there is no sequence of length 2$2$ having sum of elements equal to 1$1$, so there is no such interesting sequence.
• In the fourth test case, 𝑝1=𝑝2=𝑝3=0$p_1=p_2=p_3=0$, because bitwise XOR of an empty sequence is 0$0$.