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.

Samples

5
10 3 2
5 2 1
4 2 1
7 7 3
6 1 1

YES
6
3 1 1 1 1 3
NO
YES
2
2 2
YES
1
7
NO