There is a long straight road of length $$$\ell$$$ meters, where position $$$p$$$ denotes the point on the road that is $$$p$$$ meters away from the starting point. Along this road, there are $$$n$$$ buses moving in the positive direction, each traveling at the same constant speed of $$$x$$$ meters per minute. The $$$i$$$-th bus is currently at position $$$s_i$$$ and continues moving until it reaches its designated destination at position $$$t_i$$$. Once a bus reaches its destination, it ceases operation and all passengers must disembark.

There are also $$$m$$$ people who wish to reach the end of the road (position $$$\ell$$$). The current position of the $$$i$$$-th person is $$$p_i$$$, and each person can walk at a speed of at most $$$y$$$ meters per minute. If a person is at the same position as a bus, they may hop on the bus instantly. While riding a bus, they may hop off at any moment. The time required to board or leave a bus is considered negligible. Buses always move at a constant speed $$$x$$$ and never wait for passengers.

Your task is to determine the minimum possible time for each person to reach the end of the road.

$\text{[math]}$ Figure 1: An illustration for sample input 1.

Input

The first line contains five integers $$$n$$$, $$$m$$$, $$$\ell$$$, $$$x$$$ and $$$y$$$, representing the number of buses, the number of people, the length of the road, the speed of the buses, and the walking speed of the people, respectively.

The $$$i$$$-th of the following $$$n$$$ lines contains two integers $$$s_i$$$ and $$$t_i$$$, representing the starting position and the destination position of the $$$i$$$-th bus.

The $$$i$$$-th of the following $$$m$$$ lines contains one integer $$$p_i$$$, representing the current position of the $$$i$$$-th person.

$$$1 \leq n \leq 2 \times 10^5$$$
$$$1 \leq m \leq 2 \times 10^5$$$
$$$1 \leq \ell \leq 10^9$$$
$$$1 \leq y \lt x \leq 10^6$$$
$$$0 \leq s_i \lt t_i \leq \ell$$$
$$$0 \leq p_i \leq \ell$$$

Output

Print $$$m$$$ lines. The $$$i$$$-th line contains a number which is the minimum time (in minutes) for the $$$i$$$-th person to reach the end of the road.

Your answer will be accepted if the absolute or relative error does not exceed $$$10^{-6}$$$. Formally, let your answer be $$$a$$$, and the jury's answer be $$$b$$$. Your answer is considered correct if $$$\frac{\left\vert a - b \right\vert}{\max(1, \left\vert b \right\vert)} \leq 10^{-6}$$$.

Note

Explanation of Sample 1: A person initially at position $$$p = 3$$$ can reach the end of the road in $$$6.25$$$ minutes as follows:

Wait for Bus 1 to arrive.
Hop on the bus and ride it until it reaches its destination at position $$$t_1 = 5$$$.
Get off the bus and walk the remaining distance to position $$$\ell = 10$$$.

As shown in Figure 1, the total time spent is $$$6.25$$$ minutes, which is the minimum possible.

Buses

Examples