Codeforces Round 970 (Div. 3) |
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Finished |
Sakurako has prepared a task for you:
She gives you an array of n integers and allows you to choose i and j such that i≠j and ai≥aj, and then assign ai=ai−aj or ai=ai+aj. You can perform this operation any number of times for any i and j, as long as they satisfy the conditions.
Sakurako asks you what is the maximum possible value of mexk∗ of the array after any number of operations.
∗mexk is the k-th non-negative integer that is absent in the array. For example, mex1({1,2,3})=0, since 0 is the first element that is not in the array, and mex2({0,2,4})=3, since 3 is the second element that is not in the array.
The first line contains a single integer t (1≤t≤104) — the number of test cases.
The first line of each test case contains two integers n and k (1≤n≤2⋅105,1≤k≤109) — the number of elements in the array and the value k for mexk.
The second line of each test case contains n integers a1,a2,…,an (1≤ai≤109) — the elements of the array.
It is guaranteed that the sum of n across all test cases does not exceed 2⋅105.
For each test case, output the maximum mexk that can be achieved through the operations.
61 332 101 13 11 2 33 21 2 44 52 2 2 164 52 2 2 3
2 11 3 4 8 8
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