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.

Input

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 $$$x$$$ ($$$1 \le x \le k \le n \le 100$$$).

Output

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.

Note

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.

Forbidden Integer

Examples