You are given an array a of n positive integers and an integer x. You can do the following two-step operation any (possibly zero) number of times:
Find the maximum value of the MEX of a if you perform the operations optimally.
The MEX (minimum excluded value) of an array is the smallest non-negative integer that is not in the array. For example:
Each test contains multiple test cases. The first line contains the number of test cases t (1≤t≤5000). The description of the test cases follows.
The first line of each test case contains two integers n and x (1≤n≤2⋅105; 1≤x≤109) — the length of the array and the integer to be used in the operation.
The second line of each test case contains n integers a1,a2,…,an (0≤ai≤109) — the given array.
It is guaranteed that the sum of n over all test cases does not exceed 2⋅105.
For each test case, output a single integer: the maximum MEX of a if you perform the operations optimally.
36 30 3 2 1 5 26 21 3 4 1 0 24 52 5 10 3
4 6 0
In the first test case, the MEX of a is 4 without performing any operations, which is the maximum.
In the second test case, the MEX of a is 5 without performing any operations. If we perform two operations both with i=1, we will have the array a=[5,3,4,1,0,2]. Then, the MEX of a will become 6, which is the maximum.
In the third test case, the MEX of a is 0 without performing any operations, which is the maximum.
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