Score : $400$ points

问题描述

对于 $T$ 个测试用例，解决以下问题。

给定非负整数 $a$ 和 $s$。是否存在一对非负整数 $(x, y)$ 满足以下两个条件？

• $x\ \text{AND}\ y=a$
• $x+y=s$

什么是按位 $\mathrm{AND}$？

整数 $A$ 和 $B$ 的按位 $\mathrm{AND}$（记作 $A\ \mathrm{AND}\ B$）定义如下：

• 当 $A\ \mathrm{AND}\ B$ 以二进制形式表示时，在 $2^k$ 位（$k \geq 0$）上的数字是：如果 $A$ 和 $B$ 在该位上都是 $1$，则为 $1$，否则为 $0$。

例如，我们有 $4\ \mathrm{AND}\ 6 = 4$（以二进制表示：$100\ \mathrm{AND}\ 110 = 100$）。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Solve the following problem for $T$ test cases.

Given are non-negative integers $a$ and $s$. Is there a pair of non-negative integers $(x,y)$ that satisfies both of the conditions below?

• $x\ \text{AND}\ y=a$
• $x+y=s$

What is bitwise $\mathrm{AND}$?

The bitwise $\mathrm{AND}$ of integers $A$ and $B$, $A\ \mathrm{AND}\ B$, is defined as follows:

• When $A\ \mathrm{AND}\ B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if those of $A$ and $B$ are both $1$, and $0$ otherwise.

For example, we have $4\ \mathrm{AND}\ 6 = 4$ (in base two: $100\ \mathrm{AND}\ 110 = 100$).

Constraints

• $1 \leq T \leq 10^5$
• $0 \leq a,s \lt 2^{60}$
• All values in input are integers.

Input

Input is given from Standard Input. The first line is in the following format:

$T$

Then, $T$ test cases follow. Each test case is in the following format:

$a$ $s$

Output

Print $T$ lines. The $i$-th line $(1 \leq i \leq T)$ should contain Yes if, in the $i$-th test case, there is a pair of non-negative integers $(x,y)$ that satisfies both of the conditions in the Problem Statement, and No otherwise.

Sample Input 1

2
1 8
4 2

Sample Output 1

Yes
No

In the first test case, some pairs such as $(x,y)=(3,5)$ satisfy the conditions.

In the second test case, no pair of non-negative integers satisfies the conditions.

Sample Input 2

4
201408139683277485 381410962404666524
360288799186493714 788806911317182736
18999951915747344 451273909320288229
962424162689761932 1097438793187620758

Sample Output 2

No
Yes
Yes
No

update @ 2024/3/10 10:17:23