You are given a set $S$ consisting of $n+1$ non-negative integers, $S = {0, 1, ..., n }$. Also, you have $k$ unlucky integers $x_1, x_2, \dots x_k.$

Let's denote the $X$- misfortune of the set $S$, $f(S, X)$ --- the number of pairs of integers $(a, b)$ such that $a + b = X, a \ne b$ and   $a \in S, b \in S$. RedDreamer has to paint each element of $S$ into one of two colors, white and black, and then create two sets $c$ and $d$ so that all white elements belong to $c$, and all the black elements belong to $d$ (it is possible that one of these two sets becomes empty). RedDreamer wants to paint the elements in such a way that $\sum_{i=1}^{k} |f(c, x_i) - f(d, x_i)|$ is minimum possible.

Help RedDreamer to paint the set optimally!

Input format

• The first line contains one integer $t (1≤t≤1000)$ — the number of test cases. 
• The first line of each test case contains two integers $n$ and $k (1 ≤ n ≤ 10^5 , 0 ≤ k ≤ 1000)$
• The second line of each test case contains k integers $x_1, x_2, . . . , x_n (0 ≤ x_i ≤ n).$

Note: The sum of $n$ test cases does not exceed $10^5$.

Output format

• For each test case print $n$ integers, $p_0, p_1, p_2, . . . , p_n$ (each $p_i$ is either 0 or 1) denoting the colors. If $i$ is 0, then $i$ is white and belongs to the set $c$, otherwise, it is black and belongs to the set $d$
• If there are multiple answers that minimize the value of $\sum_{i=1}^{k} |f(c, x_i) - f(d, x_i)|$, print any of them.