Nastia and Nearly Good Numbers

1000ms

262144K

Description:

Nastia has $$$2$$$ positive integers $$$A$$$ and $$$B$$$. She defines that:

The integer is good if it is divisible by $$$A \cdot B$$$;
Otherwise, the integer is nearly good, if it is divisible by $$$A$$$.

For example, if $$$A = 6$$$ and $$$B = 4$$$, the integers $$$24$$$ and $$$72$$$ are good, the integers $$$6$$$, $$$660$$$ and $$$12$$$ are nearly good, the integers $$$16$$$, $$$7$$$ are neither good nor nearly good.

Find $$$3$$$ different positive integers $$$x$$$, $$$y$$$, and $$$z$$$ such that exactly one of them is good and the other $$$2$$$ are nearly good, and $$$x + y = z$$$.

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10\,000$$$) — the number of test cases.

The first line of each test case contains two integers $$$A$$$ and $$$B$$$ ($$$1 \le A \le 10^6$$$, $$$1 \le B \le 10^6$$$) — numbers that Nastia has.

Output:

For each test case print:

"YES" and $$$3$$$ different positive integers $$$x$$$, $$$y$$$, and $$$z$$$ ($$$1 \le x, y, z \le 10^{18}$$$) such that exactly one of them is good and the other $$$2$$$ are nearly good, and $$$x + y = z$$$.
"NO" if no answer exists.

You can print each character of "YES" or "NO" in any case.

If there are multiple answers, print any.

Sample Input:

Sample Output:

YES
10 50 60
YES
169 39 208
YES
28 154 182

Note:

In the first test case: $$$60$$$ — good number; $$$10$$$ and $$$50$$$ — nearly good numbers.

In the second test case: $$$208$$$ — good number; $$$169$$$ and $$$39$$$ — nearly good numbers.

In the third test case: $$$154$$$ — good number; $$$28$$$ and $$$182$$$ — nearly good numbers.

Informação

Provedor Codeforces

Código CF1521A