102383: [AtCoder]ABC238 D - AND and SUM
Description
Score : $400$ points
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.
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
Input
题意翻译
给出两个数 $a,b$，问能否找到两个数 $x$ 和 $y$ 使得 $x+y=a$ 且 $x\ \operatorname{and}\ y=b$。 多组数据询问。Output
得分：400分
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$(x,y)$，同时满足以下两个条件？
- $x\ \text{AND}\ y=a$
- $x+y=s$
什么是按位与？
整数$A$和$B$的按位与$A\ \mathrm{AND}\ B$定义如下：
- 当$A\ \mathrm{AND}\ B$用二进制表示时，第$2^k$位（$k \geq 0$）为$1$，当$A$和$B$的该位均为$1$时，否则为$0$。
约束条件
- $1 \leq T \leq 10^5$
- $0 \leq a,s \lt 2^{60}$
- 输入中的所有值都是整数。
输入
输入从标准输入给出。第一行是以下格式：
$T$
接着，$T$个测试用例跟在后面。每个测试用例是以下格式：
$a$ $s$
输出
打印$T$行。第$i$行$(1 \leq i \leq T)$应包含Yes，如果在第$i$个测试用例中，存在一对非负整数$(x,y)$同时满足问题描述中的两个条件，否则包含No。
样例输入1
2 1 8 4 2
样例输出1
Yes No
在第一个测试用例中，存在一些满足条件的对$(x,y)$，例如$(x,y)=(3,5)$。
在第二个测试用例中，不存在一对非负整数满足条件。
样例输入2
4 201408139683277485 381410962404666524 360288799186493714 788806911317182736 18999951915747344 451273909320288229 962424162689761932 1097438793187620758
样例输出2
No Yes Yes No