Description

Given integers $n$ and $m$, determine whether there is a sequence $a$ that satisfying the following constraints. The indices of the sequence elements in this question start from $1$.

• The length of the sequence $a$ is $m$, and each entry of the sequence $a$ is a positive integer.

• $a_1 \oplus a_2 \oplus \cdots \oplus a_m = n$, that is, the result of XORing all entries of the sequence $a$ is equal to $n$.

• All the entries in $a$ are the same.

Input Format

Each test consists of multiple test cases.

The first line contains an integer $T$ — the number of test cases. Then follows the description of the test cases.

Each test case consists of one line. The only line of each test case contains two integers $n$ and $m$.

Output Format

For each test case, if there is a sequence $a$ that satisfies the restrictions, print Yes; otherwise, print No.

4
3 3
2 5
0 3
1 4

Yes
Yes
No
No

Hint

「Sample Explanation #1」

For the first test case, the sequence $a$ can be $[3,3,3]$, in which case $a_1 \oplus a_2 \oplus a_3 = 3 \oplus 3 \oplus 3 = 3$.

For the second test case, the sequence $a$ can be $[2,2,2,2,2]$, in which case $a_1 \oplus a_2 \oplus a_3 \oplus a_4 \oplus a_5 = 2 \oplus 2 \oplus 2 \oplus 2 \oplus 2 = 2$.

For the third and fourth test cases, it can be proved that there is no sequence that satisfies the restrictions.

「Constraints」

Each test is worth $20$ points.

For all tests, $1 \leq T \leq 10^5$, $0 \leq n \leq 10^9$, $2 \leq m \leq 10^9$.