will play out the accompanying activity k occasions: Add the component ⌈a+b2⌉ (gathered together) into S, where a=mex(S) and b=max(S). If this number is as of now in the set, it is added once more. Here max of a multiset indicates the greatest integer in the multiset, and mex of a multiset
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You will play out the accompanying activity k occasions:
Add the component ⌈a+b2⌉ (gathered together) into S, where a=mex(S) and b=max(S). If this number is as of now in the set, it is added once more.
Here max of a multiset indicates the greatest integer in the multiset, and mex of a multiset signifies the littlest non-negative integer that is absent in the multiset. For instance:
mex({1,4,0,2})=3;
mex({2,5,1})=0.
Your undertaking is to work out the number of particular components in S after k tasks will be finished.
Input
The input comprises of different experiments. The main line contains a solitary integer t (1≤t≤100) — the number of experiments. The portrayal of the experiments follows.
The primary line of each experiment contains two integers n, k (1≤n≤105, 0≤k≤109) — the underlying size of the multiset S and the number of tasks you wanted to perform.
The second line of each experiment contains n particular integers a1,a2,… ,an (0≤
It is ensured that the amount of n over all experiments doesn't surpass 105.
Output
For each experiment, print the number of unmistakable components in S after k tasks will be finished.
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