You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
You are given an array of exactly $$$n$$$ numbers $$$[1,2,3,\ldots,n]$$$ along with integers $$$k$$$ and $$$x$$$.

Partition the array in exactly $$$k$$$ non-empty disjoint subsequences such that the bitwise XOR of all numbers in each subsequence is $$$x$$$, and each number is in exactly one subsequence. Notice that there are no constraints on the length of each subsequence.

A sequence $$$a$$$ is a subsequence of a sequence $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by the deletion of several (possibly, zero or all) elements.

For example, for $$$n = 15$$$, $$$k = 6$$$, $$$x = 7$$$, the following scheme is valid:

- $$$[6,10,11]$$$, $$$6 \oplus 10 \oplus 11 = 7$$$,
- $$$[5,12,14]$$$, $$$5 \oplus 12 \oplus 14 = 7$$$,
- $$$[3,9,13]$$$, $$$3 \oplus 9 \oplus 13 = 7$$$,
- $$$[1,2,4]$$$, $$$1 \oplus 2 \oplus 4 = 7$$$,
- $$$[8,15]$$$, $$$8 \oplus 15 = 7$$$,
- $$$[7]$$$, $$$7 = 7$$$,

The following scheme is invalid, since $$$8$$$, $$$15$$$ do not appear:

- $$$[6,10,11]$$$, $$$6 \oplus 10 \oplus 11 = 7$$$,
- $$$[5,12,14]$$$, $$$5 \oplus 12 \oplus 14 = 7$$$,
- $$$[3,9,13]$$$, $$$3 \oplus 9 \oplus 13 = 7$$$,
- $$$[1,2,4]$$$, $$$1 \oplus 2 \oplus 4 = 7$$$,
- $$$[7]$$$, $$$7 = 7$$$.

The following scheme is invalid, since $$$3$$$ appears twice, and $$$1$$$, $$$2$$$ do not appear:

- $$$[6,10,11]$$$, $$$6 \oplus 10 \oplus 11 = 7$$$,
- $$$[5,12,14]$$$, $$$5 \oplus 12 \oplus 14 = 7$$$,
- $$$[3,9,13]$$$, $$$3 \oplus 9 \oplus 13 = 7$$$,
- $$$[3,4]$$$, $$$3 \oplus 4 = 7$$$,
- $$$[8,15]$$$, $$$8 \oplus 15 = 7$$$,
- $$$[7]$$$, $$$7 = 7$$$.

## Input Format
Each test contains multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first and the only line of each test case contains three integers $$$n$$$, $$$k$$$, $$$x$$$ ($$$1 \le k \le n \le 2 \cdot 10^5$$$; $$$1\le x \le 10^9$$$) — the length of the array, the number of subsequences and the required XOR.

It's guaranteed that the sum of $$$n$$$ does not exceed $$$2 \cdot 10^5$$$.

## Output Format
For each test case, if it is possible to partition the sequence, print "YES" in the first line. In the $$$i$$$-th of the following $$$k$$$ lines first print the length $$$s_i$$$ of the $$$i$$$-th subsequence, then print $$$s_i$$$ integers, representing the elements in the $$$i$$$-th subsequence. If there are multiple answers, print any. Note that you can print a subsequence in any order.

If it is not possible to partition the sequence, print "NO".

## Examples
```input
7
15 6 7
11 4 5
5 3 2
4 1 4
6 1 7
11 5 5
11 6 5
```
```output
YES
3 6 10 11
3 5 12 14
3 3 9 13
3 1 2 4
2 8 15
1 7
YES
2 1 4
2 2 7
2 3 6
5 5 8 9 10 11
NO
YES
4 1 2 3 4
YES
6 1 2 3 4 5 6
NO
NO
```

## Note
In the first test case, we construct the following $$$6$$$ subsequences:

- $$$[6,10,11]$$$, $$$6 \oplus 10 \oplus 11 = 7$$$,
- $$$[5,12,14]$$$, $$$5 \oplus 12 \oplus 14 = 7$$$,
- $$$[3,9,13]$$$, $$$3 \oplus 9 \oplus 13 = 7$$$,
- $$$[1,2,4]$$$, $$$1 \oplus 2 \oplus 4 = 7$$$,
- $$$[8,15]$$$, $$$8 \oplus 15 = 7$$$,
- $$$[7]$$$, $$$7 = 7$$$.

In the second test case, we construct the following $$$4$$$ subsequences:

- $$$[1,4]$$$, $$$1 \oplus 4 = 5$$$,
- $$$[2,7]$$$, $$$2 \oplus 7 = 5$$$,
- $$$[3,6]$$$, $$$3 \oplus 6 = 5$$$,
- $$$[5,8,9,10,11]$$$, $$$5 \oplus 8 \oplus 9 \oplus 10 \oplus 11 = 5$$$.

The following solution is considered correct in this test case as well:

- $$$[1,4]$$$, $$$1 \oplus 4 = 5$$$,
- $$$[2,7]$$$, $$$2 \oplus 7 = 5$$$,
- $$$[5]$$$, $$$5 = 5$$$,
- $$$[3,6,8,9,10,11]$$$, $$$3 \oplus 6 \oplus 8 \oplus 9 \oplus 10 \oplus 11 = 5$$$.

Now solve the problem and return the code.