1521A - Nastia and Nearly Good Numbers.cpp

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

The integer is good if it is divisible by A·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=t=10000) — the number of test cases.

The first line of each test case contains two integers A and B (1=A=106, 1=B=106) — numbers that Nastia has.

Output
For each test case print:

"YES" and 3 different positive integers x, y, and z (1=x,y,z=1018) 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.

Example
inputCopy
3
5 3
13 2
7 11
outputCopy
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.
*/




#include<bits/stdc++.h>
using namespace std;
 
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    
    int t;
    cin >> t;
    
    while (t--) {
    	long long a, b;
    	cin >> a >> b;
    	
    	if (b == 1) cout << "NO" << endl;
    	else cout << "YES" << endl << a * b << " " << a << " " << a * b + a << endl;
	}
  	
    return 0;
}