#AT2064. D - AND and SUM
D - AND and SUM
当前没有测试数据。
D - AND and SUM
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:
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.
2
1 8
4 2
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.
4
201408139683277485 381410962404666524
360288799186493714 788806911317182736
18999951915747344 451273909320288229
962424162689761932 1097438793187620758
No
Yes
Yes
No