You are given an integer $$$n$$$, which you want to obtain. You have an unlimited supply of every integer from $$$1$$$ to $$$k$$$, except integer $$$x$$$ (there are no integer $$$x$$$ at all).
You are allowed to take an arbitrary amount of each of these integers (possibly, zero). Can you make the sum of taken integers equal to $$$n$$$?
If there are multiple answers, print any of them.
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of testcases.
The only line of each testcase contains three integers $$$n, k$$$ and $$$x$$$ ($$$1 \le x \le k \le n \le 100$$$).
For each test case, in the first line, print "YES" or "NO" — whether you can take an arbitrary amount of each integer from $$$1$$$ to $$$k$$$, except integer $$$x$$$, so that their sum is equal to $$$n$$$.
If you can, the second line should contain a single integer $$$m$$$ — the total amount of taken integers. The third line should contain $$$m$$$ integers — each of them from $$$1$$$ to $$$k$$$, not equal to $$$x$$$, and their sum is $$$n$$$.
If there are multiple answers, print any of them.
510 3 25 2 14 2 17 7 36 1 1
YES 6 3 1 1 1 1 3 NO YES 2 2 2 YES 1 7 NO
Another possible answer for the first testcase is $$$[3, 3, 3, 1]$$$. Note that you don't have to minimize the amount of taken integers. There also exist other answers.
In the second testcase, you only have an unlimited supply of integer $$$2$$$. There is no way to get sum $$$5$$$ using only them.
In the fifth testcase, there are no integers available at all, so you can't get any positive sum.