C. Doremy's IQ
time limit per test
1 second
memory limit per test
256 megabytes
standard input
standard output

Doremy is asked to test $$$n$$$ contests. Contest $$$i$$$ can only be tested on day $$$i$$$. The difficulty of contest $$$i$$$ is $$$a_i$$$. Initially, Doremy's IQ is $$$q$$$. On day $$$i$$$ Doremy will choose whether to test contest $$$i$$$ or not. She can only test a contest if her current IQ is strictly greater than $$$0$$$.

If Doremy chooses to test contest $$$i$$$ on day $$$i$$$, the following happens:

  • if $$$a_i>q$$$, Doremy will feel she is not wise enough, so $$$q$$$ decreases by $$$1$$$;
  • otherwise, nothing changes.
If she chooses not to test a contest, nothing changes.

Doremy wants to test as many contests as possible. Please give Doremy a solution.


The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1\le t\le 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line contains two integers $$$n$$$ and $$$q$$$ ($$$1 \le n \le 10^5$$$, $$$1 \le q \le 10^9$$$) — the number of contests and Doremy's IQ in the beginning.

The second line contains $$$n$$$ integers $$$a_1,a_2,\cdots,a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the difficulty of each contest.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.


For each test case, you need to output a binary string $$$s$$$, where $$$s_i=1$$$ if Doremy should choose to test contest $$$i$$$, and $$$s_i=0$$$ otherwise. The number of ones in the string should be maximum possible, and she should never test a contest when her IQ is zero or less.

If there are multiple solutions, you may output any.

1 1
2 1
1 2
3 1
1 2 1
4 2
1 4 3 1
5 2
5 1 2 4 3

In the first test case, Doremy tests the only contest. Her IQ doesn't decrease.

In the second test case, Doremy tests both contests. Her IQ decreases by $$$1$$$ after testing contest $$$2$$$.

In the third test case, Doremy tests contest $$$1$$$ and $$$2$$$. Her IQ decreases to $$$0$$$ after testing contest $$$2$$$, so she can't test contest $$$3$$$.