Problem H. Three Integers

You are given three non-negative integers $a$, $b$, and $c$. Find three positive integers $x$, $y$, and $z$ that satisfy

$$\begin{array}{c} x \text{ mod } y = a \\ y \text{ mod } z = b \\ z \text{ mod } x = c \\ \end{array} $$

Input

The first line contains an integer $t$ $\left(1 \leq t \leq 10^5 \right)$ --the number of test cases.

Each test case contains $3$ integers $a,b,c$ $\left(0 \leq a,b,c \leq 10^9 \right)$ on a single line.

Output

For each test case, if there are such three integers satisfying the condition, output "YES", then output the three integers $x,y,z$ $\left(1 \leq x,y,z \leq 10^{18} \right)$ on the following line, or "NO" otherwise.

Example

4
0 0 0
1 2 3
6 6 6
11 3 3

YES
1 1 1
YES
5 2 8
NO
YES
11 45 14

Hint

The question comes from 2021 GuangZhou but this question is used as an exercise.