Exact Marks ~ WildLife-TK

Chef attempted an exam consisting of

$N$ objective questions. The marking scheme of the exam is:

$+ 3$ marks for a correct answer.
$- 1$ marks for an incorrect answer.
$0$ marks for an unattempted question.

Find whether it is possible for Chef to score exactly $X$ marks.

If it is possible, print $3$ integers $A$ , $B$ , and $C$ denoting the number of correct answers, incorrect answers and unattempted questions respectively.

Input Format

First line will contain $T$ , number of test cases. Then the test cases follow.
Each test case contains of a single line of input, two integers $N, X$ .

Output Format

For each test case, print $YES$ if it is possible to score exactly $X$ marks, otherwise print $NO$ .

If the answer is $YES$ , print $3$ integers $A$ , $B$ and $C$ in the next line such that:

$0 \leq A, B, C \leq N$
$A + B + C = N$
Chef's total score is exactly $X$ .

In case of multiple answers, every valid tuple is accepted.

You may print each character of the string in uppercase or lowercase (for example, the strings $yEs$ , $yes$ , $Yes$ and $YES$ will all be treated as identical).

Constraints

$1 \leq T \leq 1000$
$1 \leq N \leq 10^{8}$
$0 \leq X \leq 3 \cdot N$

Sample Input 1

Sample Output 1

YES
10 0 0
NO
YES
1 3 4

Explanation

Test Case $1$ : A possible way of scoring $30$ marks in an exam with $10$ questions is: all the $10$ answers are correct. This way the score is $10 \cdot 3 = 30$ . Thus, the values of $A, B,$ and $C$ are $10, 0,$ and $0$ respectively.

Test Case $2$ : There is no possible way to score exactly $25$ marks in an exam with $9$ questions.

Test Case $3$ : A possible way of scoring $0$ marks in an exam with $8$ questions is: $1$ answer is correct, $3$ answers are wrong and $4$ questions are unattempted. This way the score is $1 \cdot 3 + 3 \cdot (- 1) + 4 \cdot 0 = 0$ . Thus, the values of $A, B,$ and $C$ are $1, 3,$ and $4$ respectively.

Exact Marks