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.