Kevin has recently learned the definition of variance. For an array (a) of length (n), the variance of (a) is defined as follows: Let (x=\dfrac{1}{n}\displaystyle\sum_{i=1}^n a_i), i.e., (x) is the mean of the array (a); Then, the variance of (a) is () V(a)=\frac{1}{n}\sum_{i=1}^n(a_i-x)^2. () Now, Kevin gives you an array (a) consisting of (n) integers, as well as an integer (k). You can perform the following operation on (a): Select an interval (l,r) ((1\le l\le r\le n)), then for each (l\le i\le r), increase (a_i) by (k). For each (1\le p\le m), you have to find the minimum possible variance of (a) after exactly (p) operations are performed, independently for each (p). For simplicity, you only need to output the answers multiplied by (n^2). It can be proven that the results are always integers. Each test contains multiple test cases. The first line of the input contains a single integer (t) ((1\le t\le 100)) — the number of test cases. The description of test cases follows. The first line of each test case contains three integers (n), (m), and (k) ((1\le n,m\le 5000), (\color{red}{n\cdot m\le 2\cdot 10^4}), (1\le k\le 10^5)) — the length of the array (a), the maximum number of operations, and the number you add to (a_i) each time, respectively. The second line contains (n) integers (a_1,a_2,\ldots, a_n) ((1\le a_i\le 10^5)) — the elements of the array (a). It is guaranteed that the sum of (n\cdot m) over all tests does not exceed (2\cdot 10^4). For each test case, output (m) integers in a single line, the (p)-th integer denoting the minimum possible variance of (a) when exactly (p) operations are performed, multiplied by (n^2). In the first test case: For (p = 1), you can perform the operation on (1, 1), changing (a) from (1, 2, 2) to (2, 2, 2). Since a