Codeforces Round 871 (Div. 4) |
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Finished |

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brute force

dfs and similar

dp

implementation

*1000

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D. Gold Rush

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputInitially you have a single pile with $$$n$$$ gold nuggets. In an operation you can do the following:

- Take any pile and split it into two piles, so that one of the resulting piles has exactly twice as many gold nuggets as the other. (All piles should have an integer number of nuggets.)

One possible move is to take a pile of size $$$6$$$ and split it into piles of sizes $$$2$$$ and $$$4$$$, which is valid since $$$4$$$ is twice as large as $$$2$$$.

Input

The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases.

The only line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \leq n, m \leq 10^7$$$) — the starting and target pile sizes, respectively.

Output

For each test case, output "YES" if you can make a pile of size exactly $$$m$$$, and "NO" otherwise.

You can output the answer in any case (for example, the strings "yEs", "yes", "Yes" and "YES" will be recognized as a positive answer).

Example

Input

116 49 44 218 2727 427 227 101 13 15 1746001 2984004

Output

YES YES NO NO YES YES NO YES YES NO NO

Note

The first test case is pictured in the statement. We can make a pile of size $$$4$$$.

In the second test case, we can perform the following operations: $$$\{\color{red}{9}\} \to \{\color{red}{6},3\} \to \{4,2,3\}$$$. The pile that is split apart is colored red before each operation.

In the third test case, we can't perform a single operation.

In the fourth test case, we can't end up with a larger pile than we started with.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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