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code_segments/segment_311.txt

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+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:
+
+  1. Choose an index $i$ ($1 \leq i \leq n$).    2. Increase $a_i$ by $x$, in other words $a_i := a_i + x$. 
+
+Find the maximum value of the $\operatorname{MEX}$ of $a$ if you perform the operations optimally.
+
+The $\operatorname{MEX}$ (minimum excluded value) of an array is the smallest non-negative integer that is not in the array. For example:
+
+  * The $\operatorname{MEX}$ of $[2,2,1]$ is $0$ because $0$ is not in the array.    * The $\operatorname{MEX}$ of $[3,1,0,1]$ is $2$ because $0$ and $1$ are in the array but $2$ is not.    * The $\operatorname{MEX}$ of $[0,3,1,2]$ is $4$ because $0$, $1$, $2$ and $3$ are in the array but $4$ is not.
+
+Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 5000$). The description of the test cases follows.
+
+The first line of each test case contains two integers $n$ and $x$ ($1 \le n \le 2 \cdot 10^5$; $1 \le x \le 10^9$) — the length of the array and the integer to be used in the operation.
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+The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 10^9$) — the given array.
+
+It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
+
+For each test case, output a single integer: the maximum $\operatorname{MEX}$ of $a$ if you perform the operations optimally.
+
+In the first test case, the $\operatorname{MEX}$ of $a$ is $4$ without performing any operations, which is the maximum.
+
+In the second test case, the $\operatorname{MEX}$ 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 $\operatorname{MEX}$ of $a$ will become $6$, which is the maximum.
+
+In the third test case, the $\operatorname{MEX}$ of $a$ is $0$ without performing any operations, which is the maximum.