CF2149C MEX rose

You are given an array $ a $ of length $ n $ and a number $ k $ , where $ 0 \le k \le n $ . In one operation, you can choose any index $ i $ ( $ 1 \le i \le n $ ) and set $ a_i $ to any integer value $ x $ from the range $ [0,n] $ . Find the minimum number of such operations required to satisfy the condition: $ \operatorname{MEX}(a) $ $ ^{\text{∗}} $ $ =k $ $ ^{\text{∗}} $ The minimum excluded (MEX) of a set of numbers $ a_1,a_2,\dots,a_n $ is the smallest non-negative integer $ x $ that does not appear among the $ a_i $ .

Each test consists of several sets of input data. The first line contains one integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of sets of input data. The description of the sets of input data follows. The first line of each set of input data contains two integers $ n $ and $ k $ ( $ 1 \le n \le 2 \cdot 10^5,\,\, 0 \le k \le n $ ) — the length of the array $ a $ and the required $ \operatorname{MEX}(a) $ . The second line contains $ n $ integers $ a_1,a_2,\dots,a_n $ ( $ 0 \le a_i \le n $ ) — the elements of the array $ a $ . It is guaranteed that the sum of the values of $ n $ across all sets of input data does not exceed $ 2 \cdot 10^5 $ .

For each set of input data, output one integer — the minimum number of operations required to satisfy the condition $ \operatorname{MEX}(a)=k $ .

In the first set of input data, the array $ a=[0] $ , so $ \operatorname{MEX}=1 $ . $ \\ $ By removing zero (replacing it with any $ x\in[1,n] $ ), we get $ \operatorname{MEX}=0 $ . $ \\ $ Thus, exactly one operation is required. In the third set of input data, the array contains all the numbers $ 0,1,2,3,4 $ , so $ \operatorname{MEX}(a)=5 $ from the start. Since this matches the required $ k $ , no changes are needed and the minimum number of operations is $ 0 $ .