A13651 | Zero Remainder Array

You are given an array $a$ consisting of $n$ positive integers.

Initially, you have an integer $x = 0$ . During one move, you can do one of the following two operations:

1. Choose exactly one $i$ from $1$ to $n$ and increase $a_i$ by $x$ ( $a_i := a_i + x$ ), then increase $x$ by $1$ ( $x := x + 1$ ).
2. Just increase $x$ by $1$ ( $x := x + 1$ ).

The first operation can be applied no more than once to each $i$ from $1$ to $n$ .

Your task is to find the minimum number of moves required to obtain such an array that each its element is divisible by $k$ (the value $k$ is given).

You have to answer $t$ independent test cases.

The first line of the input contains one integer $t$ ( $1 \le t \le 2 \cdot 10^4$ ) — the number of test cases. Then $t$ test cases follow.

The first line of the test case contains two integers $n$ and $k$ ( $1 \le n \le 2 \cdot 10^5; 1 \le k \le 10^9$ ) — the length of $a$ and the required divisior. The second line of the test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^9$ ), where $a_i$ is the $i$ -th element of $a$ .

It is guaranteed that the sum of $n$ does not exceed $2 \cdot 10^5$ ( $\sum n \le 2 \cdot 10^5$ ).

For each test case, print the answer — the minimum number of moves required to obtain such an array that each its element is divisible by $k$ .