Time Limit:1000ms Memory Limit:65536KB

Description

Given a triangle ABC and a point O in the triangle or on the edge of the triangle.
Link OA, OB, OC, we obtain three small triangles : OBC, OCA, OAB
we say that (S_OBC/S, S_OCA/S, S_OAB/S) is the area coordinates of O, where S
is the area of triangle ABC, and S_OBC is the area of triangle OBC, and
S_OCA, S_OAB are similar
Given A,B,C,O, what's the area coordinates of O?

Input

One test case.
The first line is 6 float number Ax Ay Bx By Cx Cy, where (Ax, Ay) is the coordinates of point A
and (Bx, By), (Cx, Cy) are similar.
ABC is in a counter-clockwise order.
The six number are in the range of [-1000 1000]
In each of the next lines, there are two float number x, y, which are the coordinates
of O, and you are expected to calculate the area coordinates of it.
O is in ABC or on the edge of ABC.

Output

For each O, output the area coordiates of it.
Accurate to two decimal places.

Sample Input

0 0 0 1 1 0
0 0

Sample Output

1.00 0.00 0.00

Hint

Do not output -0.00.
The accuracy is 1e-6.

Author

baihacker

Source