Description

Find three distinct positive integers $x,y,z(x\gt y\gt z)$ such that, for any two of them, their sum is divisible by the third number.

Now you are given several types of requirements as follows:

• Given the value of $x-y$, find $x,y,z$.
• Given the value of $x-z$, find $x,y,z$.
• Given the value of $y-z$, find $x,y,z$.

Input Format

There are $T+1$ lines in total.

The first line contains an integer $T$, indicating that there are $T$ test cases.

The next $T$ lines each contain two items:

1. A string, which can be $x-y$, $x-z$, or $y-z$, indicating which two numbers were subtracted to obtain the given value.
2. A number, the value of this difference.

Output Format

There are $T$ lines in total.

Each line outputs three positive integers $x,y,z$ (as described above). The problem guarantees that a solution exists.

1
x-y 1

3 2 1

Hint

Sample Explanation

From $x-y=1$, we know that the difference between $x$ and $y$ is $1$. After trying, we get $x=3,y=2,z=1$.

It is then clear that $z\mid (x+y)$, $y\mid (x+z)$, and $x\mid (y+z)$.

Constraints

• For $1\%$ of the testdata, i.e., Sample #1.
• For $100\%$ of the testdata, $1\le T\le 10^6,1\le x,y,z\le10^8$.

Translated by ChatGPT 5