URI Online Judge | 1693

Just Another Physics Problem

By Time da UFCG BR Brazil

Timelimit: 4

Rafael Richman is a realy rich kid. He's about to make 34 years old and for his next bithday gift he asked a water arena to play with his friends. The arena consists of a flat circular field with radius R. In the middle of the field there is a tower with a height H. At the top of the tower there is a cannon that launches water with inicial velocity V. To make things more interesting, his mother Matilda Richman bought a device that changes the gravity G of the arena.

Given all the information about the arena, your task is to determine if the water thrown from the cannon can reach out the field.

You can consider that the difference between the reach of the cannon and the radius is always bigger than 0.01.

Rafael is a physics lover, and he can give you the necessary equations to solve the problem:

X(t) = Vcos(a)t
Y(t) = Vsen(a)t - GtĀ²/2

Where X and Y are the coordinates of the water in function of t, the elapsed time since the water came out of the cannon and "a" is the angle with the horizontal.

Input

There are several tests cases. Each test case is given using a single line. Each line contains 4 integers, R, H, V and G. All the integers are greater than 0 and smaller or equal than 10000. All the distance units are given in meters and all the time units are given in seconds.

Output

For each test case output output a single line containing 'Y' if the reach of the cannon is bigger than the radius of the field, or 'N' otherwise.

Sample Input Sample Output

1 1 1 1
100 100 100 100
100 100 1 100

Y
Y
N