Tribute

The Son of Heaven, our beloved emperor, has commanded you, his First Minister, to extort tribute from $n$ neighbouring kingdoms. Each tributary has been assigned a number of silver coins to pay: for the $i$-th kingdom, the number is $a_i$. To show His infinite grace, the emperor decided to take money from only some of the countries and spare the rest. Your overzealous finance minister, after writing down all $a_i$, has already produced all possible $2^n - 1$ income values, the sums of the non-empty subsets of tributaries. Unfortunately, in the process the minister lost the paper sheet with the original tribute values. For this infraction, as well as improper calligraphy, he was promptly executed.

Now you have only $2^n - 1$ sums, written rather badly. Can you recover the tribute values from them?

The first line of input contains the number of test cases $z$ $(1 \leq z \leq 200)$. The descriptions of the test cases follow.

Every test case consists of two lines: the first contains a number $n$ $(1 \le n \le 20)$, the second contains $2^n -1$ integers not exceeding $2 \cdot 10^9$, denoting all the possible sums of tributes. Assume that the tribute values were all positive integers. The total number of sums in all test cases does not exceed $10^7$.

For each test case output the recovered values of $a_i$ for $i = 1, 2, \ldots, n$, in increasing order. If there are no values that fit the input, or if there are multiple possibilities, simply write ``\texttt{NO}'' instead: you cannot execute anyone twice.