Description

Input

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 $2 \cdot 10^5$.

Output

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

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

2
2
1
0
2
0
1
2
0
1
1
4
0
4
3

Note

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 $60$.