A. Doremy's IQtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputDoremy 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.InputThe 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.OutputFor 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.ExampleInput
51 112 11 23 11 2 14 21 4 3 15 25 1 2 4 3Output
1
11
110
1110
01111
NoteIn 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.
51 112 11 23 11 2 14 21 4 3 15 25 1 2 4 3
1 11 110 1110 01111 
['binary search', 'constructive algorithms', 'greedy', 'implementation', '*1600']