[Solution] Doremy's IQ Codeforces Solution

C. Doremy's IQ

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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

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

• if ai>q$a_i>q$, Doremy will feel she is not wise enough, so q$q$ decreases by 1$1$;
• 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.

Input

The input consists of multiple test cases. The first line contains a single integer t$t$ (1≤t≤104$1\le t\le {10}^4$) — the number of test cases. The description of the test cases follows.

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The first line contains two integers n$n$ and q$q$ (1≤n≤105$1\le n\le {10}^5$, 1≤q≤109$1\le q\le {10}^9$) — the number of contests and Doremy's IQ in the beginning.

The second line contains n$n$ integers a1,a2,⋯,an$a_1,a_2,\cdots ,a_n$ (1≤ai≤109$1\le a_i\le {10}^9$) — the difficulty of each contest.

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It is guaranteed that the sum of n$n$ over all test cases does not exceed 105${10}^5$.

Output

For each test case, you need to output a binary string s$s$, where si=1$s_i=1$ if Doremy should choose to test contest i$i$, and si=0$s_i=0$ 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.