Description

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line of each test case contains two integers $n$, $k$ ($1 \le n \le 2 \cdot 10^5$, $1 \leq k \leq 10^{12}$) — the number of integers initially on the blackboard and the constant $k$.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^{12}$) — the initial state of the blackboard.

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 a single line containing an integer: the minimum number of operations you need to make all the numbers on the blackboard equal, or $-1$ if it is impossible.

9
2 1
3 4
2 3
7 11
3 10
100 40 100
2 1
1 2
2 2
1 2
1 327869541
327869541
5 26250314066
439986238782 581370817372 409476934981 287439719777 737637983182
5 616753575719
321037808624 222034505841 214063039282 441536506916 464097941819
5 431813672576
393004301966 405902283416 900951084746 672201172466 518769038906

3
1
4
-1
-1
0
3119
28999960732
-1

Note

In the first test case, $k = 1$. You can make all the numbers on the blackboard equal to $2$ with the following operations:

• Erase $x = 4$ and write $(y, z) = (2, 3)$. Note that $y+z=x+k$. The blackboard now contains the multiset $\{3, 2, 3\}$.
• Erase $x = 3$ and write $(y, z) = (2, 2)$. Note that $y+z=x+k$. The blackboard now contains $\{2, 2, 2, 3\}$.
• Erase $x = 3$ and write $(y, z) = (2, 2)$. Note that $y+z=x+k$. The blackboard now contains $\{2, 2, 2, 2, 2\}$.

This makes all the numbers equal in $3$ operations. It can be shown that you cannot make all the numbers equal in less than $3$ operations.

In the second test case, $k = 3$. You can make all the numbers on the blackboard equal to $7$ with the following operation:

• Erase $x = 11$ and write $(y, z) = (7, 7)$. Note that $y+z=x+k$. The blackboard now contains $\{7, 7, 7\}$.

In the third test case, $k = 10$. You can make all the numbers on the blackboard equal to $40$ with the following operations:

• Erase $x = 100$ and write $(y, z) = (70, 40)$. Note that $y+z=x+k$. The blackboard now contains $\{70, 40, 40, 100\}$.
• Erase $x = 70$ and write $(y, z) = (40, 40)$. Note that $y+z=x+k$. The blackboard now contains $\{40, 40, 40, 40, 100\}$.
• Erase $x = 100$ and write $(y, z) = (40, 70)$. Note that $y+z=x+k$. The blackboard now contains $\{40, 40, 40, 40, 40, 70\}$.
• Erase $x = 70$ and write $(y, z) = (40, 40)$. Note that $y+z=x+k$. The blackboard now contains $\{40, 40, 40, 40, 40, 40, 40\}$.

In the fourth and in the fifth test case, you can show that it is impossible to make all the numbers on the blackboard equal.