CF1883C.Raspberries

普及/提高-

通过率：0%

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题目描述

You are given an array of integers $a_1, a_2, \ldots, a_n$ and a number $k$ ( $2 \leq k \leq 5$ ). In one operation, you can do the following:

Choose an index $1 \leq i \leq n$ ,
Set $a_i = a_i + 1$ .

Find the minimum number of operations needed to make the product of all the numbers in the array $a_1 \cdot a_2 \cdot \ldots \cdot a_n$ divisible by $k$ .

输入格式

Each test consists of multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 10^4$ ) — the number of test cases. Then follows the description of the test cases.

The first line of each test case contains two integers $n$ and $k$ ( $2 \leq n \leq 10^5$ , $2 \leq k \leq 5$ ) — the size of the array $a$ and the number $k$ .

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq 10$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

输出格式

For each test case, output the minimum number of operations needed to make the product of all the numbers in the array divisible by $k$ .

输入输出样例

输入#1

15
2 5
7 3
3 3
7 4 1
5 2
9 7 7 3 9
5 5
5 4 1 2 3
7 4
9 5 1 5 9 5 1
3 4
6 3 6
3 4
6 1 5
3 4
1 5 9
4 4
1 4 1 1
3 4
3 5 3
4 5
8 9 9 3
2 5
1 6
2 5
10 10
4 5
1 6 1 1
2 5
7 7

输出#1

说明/提示

In the first test case, we need to choose the index $i = 2$ twice. After that, the array will be $a = [7, 5]$ . The product of all the numbers in the array is $35$ .

In the fourth test case, the product of the numbers in the array is $120$ , which is already divisible by $5$ , so no operations are needed.

In the eighth test case, we can perform two operations by choosing $i = 2$ and $i = 3$ in any order. After that, the array will be $a = [1, 6, 10]$ . The product of the numbers in the array is $60$ .

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