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 $a$ of $N$ ($1 \leq N \leq 2 \cdot 10^5$) non-negative integers and an integer $M$ ($1 \leq M \leq 10^9$). Then, FJ will ask Bessie for an integer $x$. In one operation, FJ can pick an index $i$ and subtract or add $1$ to $a_i$. FJ's boredom value is the minimum number of operations he must perform so that $a_i-x$ is divisible by $M$ for all $1 \leq i \leq N$.

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

입력

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

The first line of each test case contains $N$ and $M$.

The second line of each test case contains $a_1, a_2, ..., a_N$ ($0 \leq a_i \leq 10^9$).

It is guaranteed that the sum of $N$ over all test cases does not exceed $5 \cdot 10^5$.

출력

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

예제 입력 1

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

예제 출력 1

10
21

점수

Input 2: $N \le 1000$ and $M \le 1000$.Input 3: $N\le 1000$.Inputs 4-5: $M\le 10^5$.Inputs 6-16: No additional constraints.