You are given an array $$$a$$$ of $$$n$$$ integers, where all elements $$$a_i$$$ lie in the range $$$[1, k]$$$. How many different arrays $$$b$$$ of $$$m$$$ integers, where all elements $$$b_i$$$ lie in the range $$$[1, k]$$$, contain $$$a$$$ as a subsequence? Two arrays are considered different if they differ in at least one position.

A sequence $$$x$$$ is a subsequence of a sequence $$$y$$$ if $$$x$$$ can be obtained from $$$y$$$ by the deletion of several (possibly, zero or all) elements.

Since the answer may be large, print it modulo $$$10^9 + 7$$$.

Input

The first line of the input contains a single 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 three integers $$$n$$$, $$$m$$$, $$$k$$$ ($$$1 \le n \le 2\cdot 10^5$$$, $$$n \le m \le 10^9$$$, $$$1 \le k \le 10^9$$$) — the size of $$$a$$$, the size of $$$b$$$, and the maximum value allowed in the arrays, respectively.

The next line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots a_n$$$ ($$$1\le a_i \le k$$$) — the elements of the array $$$a$$$.

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 integer — the number of suitable arrays $$$b$$$, modulo $$$10^9+7$$$.

Note

For the first example, since $$$k=1$$$, there is only one array of size $$$m$$$ consisting of the integers $$$[1, k]$$$. This array ($$$[1, 1, \ldots, 1]$$$) contains the original array as a subsequence, so the answer is 1.

For the second example, the $$$9$$$ arrays are $$$[1, 1, 2, 2]$$$, $$$[1, 2, 1, 2]$$$, $$$[1, 2, 2, 1]$$$, $$$[1, 2, 2, 2]$$$, $$$[1, 2, 2, 3]$$$, $$$[1, 2, 3, 2]$$$, $$$[1, 3, 2, 2]$$$, $$$[2, 1, 2, 2]$$$, $$$[3, 1, 2, 2]$$$.

For the fourth example, since $$$m=n$$$, the only array of size $$$m$$$ that contains $$$a$$$ as a subsequence is $$$a$$$ itself.

Count Supersequences

Examples