Description:
You are given $$$n$$$ positive integers $$$x_1, x_2, \ldots, x_n$$$ and three positive integers $$$n_a, n_b, n_c$$$ satisfying $$$n_a+n_b+n_c = n$$$.
You want to split the $$$n$$$ positive integers into three groups, so that:
- The first group contains $$$n_a$$$ numbers, the second group contains $$$n_b$$$ numbers, the third group contains $$$n_c$$$ numbers.
- Let $$$s_a$$$ be the sum of the numbers in the first group, $$$s_b$$$ be the sum in the second group, and $$$s_c$$$ be the sum in the third group. Then $$$s_a, s_b, s_c$$$ are the sides of a triangle with positive area.
Determine if this is possible. If this is possible, find one way to do so.
Input Format:
Each test contains multiple test cases. The first line contains an integer $$$t$$$ ($$$1\le t\le 100\,000$$$) — the number of test cases. The descriptions of the $$$t$$$ test cases follow.
The first line of each test case contains the integers $$$n, n_a, n_b, n_c$$$ ($$$3 \leq n \leq 200\,000, 1\leq n_a,n_b,n_c \leq n-2, n_a+n_b+n_c = n$$$) — the number of integers to split into three groups, and the desired sizes of the three groups.
The second line of each test case contains $$$n$$$ integers $$$x_1, x_2, \ldots, x_n$$$ ($$$1 \leq x_i \leq 10^{9}$$$).
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$200\,000$$$.
Output Format:
For each test case, print $$$\texttt{YES}$$$ if it is possible to split the numbers into three groups satisfying all the conditions. Otherwise, print $$$\texttt{NO}$$$.
If such a split exists, then describe the three groups as follows.
On the next line, print $$$n_a$$$ integers $$$a_1, a_2, \ldots, a_{n_a}$$$ — the numbers in the first group.
On the next line, print $$$n_b$$$ integers $$$b_1, b_2, \ldots, b_{n_b}$$$ — the numbers in the second group.
On the next line, print $$$n_c$$$ integers $$$c_1, c_2, \ldots, c_{n_c}$$$ — the numbers in the third group.
These $$$n_a+n_b+n_c=n$$$ integers should be a permutation of $$$x_1, x_2, \ldots, x_n$$$, and they should satisfy the conditions from the statement.
If there are multiple solutions, print any of them.
Note:
In the first test case, we can put two $$$1$$$s into each group: the sum in each group would be $$$2$$$, and there exists a triangle with positive area and sides $$$2$$$, $$$2$$$, $$$2$$$.
In the second and third test cases, it can be shown that there is no such way to split numbers into groups.
In the fourth test case, we can put number $$$16$$$ into the first group, with sum $$$16$$$, numbers $$$12$$$ and $$$1$$$ into the second group, with sum $$$13$$$, and the remaining five $$$1$$$s into the third group, with sum $$$5$$$, as there exists a triangle with positive area and sides $$$16, 13, 5$$$.