Farmer John's Favorite Operation

문제

It is another cold and boring day on Farmer John's farm. To pass the time, Farmer John has invented a fun leisure activity involving performing operations on an integer array.

Farmer John has an array $aa$ of $NN$ ($1\le N\le 2\cdot {10}^{5}1\; \backslash leq\; N\; \backslash leq\; 2\; \backslash cdot\; 10^5$) non-negative integers and an integer $MM$ ($1\le M\le {10}^{9}1\; \backslash leq\; M\; \backslash leq\; 10^9$). Then, FJ will ask Bessie for an integer $xx$. In one operation, FJ can pick an index $ii$ and subtract or add $11$ to $a_{i}a\_i$. FJ's boredom value is the minimum number of operations he must perform so that $a_i-xa\_i-x$ is divisible by $MM$ for all $1\le i\le N1\; \backslash leq\; i\; \backslash leq\; N$.

Among all possible $xx$, output FJ's minimum possible boredom value.

입력

The first line contains $TT$ ($1\le T\le 101\; \backslash leq\; T\; \backslash leq\; 10$), the number of independent test cases to solve.

The first line of each test case contains $NN$ and $MM$.

The second line of each test case contains $a_1,a_2,\mathrm{.}\mathrm{.}\mathrm{.},a_{N}a\_1,\; a\_2,\; ...,\; a\_N$ ($0\le a_i\le {10}^{9}0\; \backslash leq\; a\_i\; \backslash leq\; 10^9$).

It is guaranteed that the sum of $NN$ over all test cases does not exceed $5\cdot {10}^{5}5\; \backslash cdot\; 10^5$.

출력

For each test case, output an integer on a new line containing FJ's minimum possible boredom value among all possible values of $xx$.

2
5 9
15 12 18 3 8
3 69
1 988244353 998244853

10
21