Inaho is taking a walk! He texts you the location he walks to from his house, which is located at the origin ~(0, 0)~ on a 2D plane. You know that the location has coordinates ~(x, y)~. However, Inaho can only walk in 2 directions: ~v~ and ~w~.

~v~ is defined as the direction from ~(0, 0)~ to ~(v_x, v_y)~, and Inaho defines that distance as 1 ~V~.

~w~ is defined as the direction from ~(0, 0)~ to ~(w_x, w_y)~, and Inaho defines that distance as 1 ~W~.

Help Inaho determine how far in each direction he must travel in order to reach his destination.

Input Specification

The first line will contain the integers ~x, y\ (-10^6 \le x, y \le 10^6)~.

The next line will contain the integers ~v_x, v_y\ (-10^6 \le v_x, v_y \le 10^6)~.

The next line will contain the integers ~w_x, w_y\ (-10^6 \le w_x, w_y \le 10^6)~.

Output Specification

Output 2 space separated real numbers, the number of ~Vs~ and ~Ws~ Inaho must travel in direction ~v~ and ~w~, respectively. It is guaranteed that there is exactly 1 distinct solution. Your output will be considered correct if it has a relative error of at most ~10^{-6}~.

Subtasks

Subtask 1 [30%]

~(-10^3 \le x, y, v_x, v_y, w_x, w_y \le 10^3)~

It is guaranteed that the number of ~Vs~ and ~Ws~ will be integers.

Subtask 2 [70%]

No further constraints.

Sample Input

9 10
1 2
3 4

Sample Output

-3 4

Explanation for Sample 1

Inaho can first travel ~-3~ ~Vs~, after which he will move ~3~ units left and ~6~ units down, ending up on the point ~(-3, -6)~. Then he can travel ~4~ ~Ws~, after which he will move ~12~ units end right and ~16~ units up, ending up on the point ~(9, 10)~.