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code_segments/segment_110.txt

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+You are given an array of integers $a_1, a_2, \ldots, a_n$ and an integer $k$. You need to make it beautiful with the least amount of operations.
+
+Before applying operations, you can shuffle the array elements as you like. For one operation, you can do the following:
+
+  * Choose an index $1 \leq i \leq n$,   * Make $a_i = a_i + k$.
+
+The array $b_1, b_2, \ldots, b_n$ is beautiful if $b_i = b_{n - i + 1}$ for all $1 \leq i \leq n$.
+
+Find the minimum number of operations needed to make the array beautiful, or report that it is impossible.
+
+Each test consists of several sets of input data. The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of sets of input data. Then follows their description.
+
+The first line of each set of input data contains two integers $n$ and $k$ ($1 \leq n \leq 10^5$, $1 \leq k \leq 10^9$) — the size of the array $a$ and the number $k$ from the problem statement.
+
+The second line of each set of input data contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$) — the elements of the array $a$.
+
+It is guaranteed that the sum of $n$ over all sets of input data does not exceed $2 \cdot 10^5$.
+
+For each set of input data, output the minimum number of operations needed to make the array beautiful, or $-1$ if it is impossible.
+
+In the first set of input data, the array is already beautiful.
+
+In the second set of input data, you can shuffle the array before the operations and perform the operation with index $i = 1$ for $83966524$ times.
+
+In the third set of input data, you can shuffle the array $a$ and make it equal to $[2, 3, 1]$. Then apply the operation with index $i = 3$ to get the array $[2, 3, 2]$, which is beautiful.
+
+In the eighth set of input data, there is no set of operations and no way to shuffle the elements to make the array beautiful.
+
+In the ninth set of input data, the array is already beautiful.