B. Nabi Puzzle
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Izumi Yuki retaliates against Kayamori Ruka's constant use of the verbal quirk teheperinko by creating a puzzle. Ruka finds herself at Nabi's ground where $$$n$$$ Nabis are arranged in a straight line. Yuki's AI assistant Ketsu reveals the challenge: assign integer values to the Nabis such that:

  • Every consecutive group of $$$p$$$ Nabis (moving left-to-right) has a positive total sum.
  • Every consecutive group of $$$q$$$ Nabis has a negative total sum.

Help Ruka solve the puzzle!

Input

Each test contains multiple tests. The first line contains one integer $$$t$$$ ($$$1\le t\le 10^4$$$) — the number of test cases. The description of each test case follows.

The only line of each test case contains three integers $$$p$$$, $$$q$$$, and $$$n$$$ ($$$1\le p, q, n\le 2\cdot 10^5$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$2\cdot 10^5$$$.

Output

For each test case:

  • If a solution exists, output "YES" in the first line, and then output $$$n$$$ integers $$$a_1,a_2,\dots,a_n$$$ ($$$|a_i|\le 10^{12}$$$) in the second line, where $$$a_i$$$ indicates the integer assigned to the $$$i$$$-th Nabi. It can be proven that if such a sequence exists, there will always be one that satisfies the given constraints.
  • If a solution doesn't exist, output "NO" in the single line.

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Example
Input
4
2 3 3
2 3 4
6 6 5
7 11 14
Output
YES
-2 3 -2
NO
YES
1 1 1 1 1
YES
1 1 5 -13 1 1 7 1 1 3 -11 1 1 7