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Contest: Task: Related: TaskC TaskE

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.
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