LiveCodeBench / 1883_C / C. Raspberries

You are given an array of integers a₁,a₂,…,a_(n) and a number k (2≤k≤5). In one operation, you can do the following:


-  Choose an index 1≤i≤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 a₁⋅a₂⋅…⋅a_(n) divisible by k.

Input

Each test consists of multiple test cases. The first line contains a single integer t (1≤t≤10⁴) — 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≤n≤10⁵, 2≤k≤5) — the size of the array a and the number k.

The second line of each test case contains n integers a₁,a₂,…,a_(n) (1≤a_(i)≤10).

It is guaranteed that the sum of n over all test cases does not exceed 2⋅10⁵.

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.Sample Input 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



Sample Output 1:

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.

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 $k$.

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 $k$.Sample Input 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



Sample Output 1:

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 $60$.