Anton came to a chocolate factory. There he found a working conveyor and decided to run on it from the beginning to the end.

The conveyor is a looped belt with a total length of 2*l* meters, of which *l* meters are located on the surface and are arranged in a straight line. The part of the belt which turns at any moment (the part which emerges from under the floor to the surface and returns from the surface under the floor) is assumed to be negligibly short.

The belt is moving uniformly at speed *v*<sub class="lower-index">1</sub> meters per second. Anton will be moving on it in the same direction at the constant speed of *v*<sub class="lower-index">2</sub> meters per second, so his speed relatively to the floor will be *v*<sub class="lower-index">1</sub> + *v*<sub class="lower-index">2</sub> meters per second. Anton will neither stop nor change the speed or the direction of movement.

Here and there there are chocolates stuck to the belt (*n* chocolates). They move together with the belt, and do not come off it. Anton is keen on the chocolates, but he is more keen to move forward. So he will pick up all the chocolates he will pass by, but nothing more. If a chocolate is at the beginning of the belt at the moment when Anton starts running, he will take it, and if a chocolate is at the end of the belt at the moment when Anton comes off the belt, he will leave it.

You are given the positions of the chocolates relative to the initial start position of the belt 0 ≤ *a*<sub class="lower-index">1</sub> &lt; *a*<sub class="lower-index">2</sub> &lt; ... &lt; *a*<sub class="lower-index">*n*</sub> &lt; 2*l*. The positions on the belt from 0 to *l* correspond to the top, and from *l* to 2*l* — to the the bottom half of the belt (see example). All coordinates are given in meters.

Anton begins to run along the belt at a random moment of time. This means that all possible positions of the belt at the moment he starts running are equiprobable. For each *i* from 0 to *n* calculate the probability that Anton will pick up exactly *i* chocolates.
The first line contains space-separated integers *n*, *l*, *v*<sub class="lower-index">1</sub> and *v*<sub class="lower-index">2</sub> (1 ≤ *n* ≤ 10<sup class="upper-index">5</sup>, 1 ≤ *l*, *v*<sub class="lower-index">1</sub>, *v*<sub class="lower-index">2</sub> ≤ 10<sup class="upper-index">9</sup>) — the number of the chocolates, the length of the conveyor's visible part, the conveyor's speed and Anton's speed.

The second line contains a sequence of space-separated integers *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub> (0 ≤ *a*<sub class="lower-index">1</sub> &lt; *a*<sub class="lower-index">2</sub> &lt; ... &lt; *a*<sub class="lower-index">*n*</sub> &lt; 2*l*) — the coordinates of the chocolates.
print("_RANDOM_GUESS_1689603884.341629")# 1689603884.3416479