No submission language available for this problem.

Description

Input

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

The first line of each test case contains two integers $n$ and $m$ ($1 \le n \le 3 \cdot 10^5, n \le m \le 10^9$) — the number of balls and the number of baskets.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le m$, $a_i$'s are pairwise distinct) — the initial position of each ball.

It is guaranteed that the sum of $n$ over all test cases does not exceed $3 \cdot 10^5$.

Output

For each test case, print one integer: the expected amount of time (in seconds) Alice needs to end the process, modulo $10^9 + 7$.

5
3 10
5 1 4
2 15
15 1
6 6
1 2 3 4 5 6
6 9
6 5 4 3 2 1
1 100
69
 
 
 
 
 
 

600000042
14
35
333333409
0

Note

In the first test case, Alice could have proceeded as follows (we define $a_i = -1$ if ball $i$ has been thrown out):

• Initially, $a = [5, 1, 4]$.
• Alice chooses $i = 2$ with probability $\frac{1}{3}$, and ball $2$ is moved to basket $2$. After this, $a = [5, 2, 4]$.
• Alice chooses $i = 2$ with probability $\frac{1}{3}$, and ball $2$ is moved to basket $3$. After this, $a = [5, 3, 4]$.
• Alice chooses $i = 2$ with probability $\frac{1}{3}$, and ball $2$ is moved to basket $4$. As basket $4$ previously contains ball $3$, this ball is thrown out. After this, $a = [5, 4, -1]$.
• Alice chooses $i = 3$ with probability $\frac{1}{3}$. Ball $3$ has already been thrown out, so nothing happens. After this, $a = [5, 4, -1]$.
• Alice chooses $i = 2$ with probability $\frac{1}{3}$, and ball $2$ is moved to basket $5$, which throws out ball $1$. After this, $a = [-1, 5, -1]$, and the process ends.

The answer for the second test case is $14$ (note that these two balls are next to each other).

The answer for the third test case is $35$.

The answer for the fourth test case is $\frac{220}{3}$.

In the fifth test case, as there is only one ball initially, the answer is $0$.