Problem Statement

You are a maid working at the maid café "Zerokan☀Taiyo". Today you are to serve a tapioca milk tea to a regular master, but just before serving it you realized that you may have accidentally put unappetizing tapioca pearls into the milk tea.

There are $N$ tapioca pearls, distinguished by the numbers $1,2,\cdots,N$. The tastiness of tapioca pearl $i$ is a positive integer $b_i$. Currently, tapioca pearls $1, 2, \cdots, M$ are in the milk tea, and all the others are in the kitchen. The tastiness of the tapioca milk tea equals the sum of the tastiness of the tapioca pearls in it.

You can use your Moe-Moe Power exactly $K$ times to teleport tapioca pearls. Each time you use the power, independently for each pearl, with probability $\frac{p}{q}$, a pearl in the milk tea moves to the kitchen, and a pearl in the kitchen moves into the milk tea. The numbers of pearls in the milk tea and in the kitchen are not necessarily preserved, the teleportation occurs independently for each pearl, and it is possible that not even $1$ pearl moves despite using the power.

After using the Moe-Moe Power exactly $K$ times, what is the expected value of the tastiness of the tapioca milk tea served to the master?

The expected value is a rational number, and under the constraints it is guaranteed that it can be expressed as $\frac{x}{y}$ with a positive integer $x$ and a positive integer $y$ that is not a multiple of $10^9+7$. Output the unique non-negative integer $R$ satisfying $0\le R \lt 10^9+7$ and $x \equiv yR \bmod{10^9+7}$.

Input

$N\ M\ K\ p\ q$
$b_1$
$b_2$
$\vdots$
$b_N$

The input satisfies the following constraints. Since the input is large, it is recommended to use a fast language such as PyPy or C++ rather than Python or the like.

• $1\le N\le 10^5$
• $0\le M\le N$
• $1\le K\le 10^{12}$
• $1\le p \lt q \le 10^9$
• $1\le b_i \le 10^9$
• All input values are integers.

Output

Output the expected value in the format described in the problem statement, followed by a newline.

Sample

1 0 1 1 2
1

500000004

4 3 4 1 4
4
4
4
4

250000010

5 2 314159265358 1729 87539319
12345678
99999996
99999997
99999998
99999999

57524728