Given a Square with vertices (0, 0) (L, 0) (L, L) (0, L,). A small (point size) ball is thrown with initial velocity v from (0, 0).

Every collision follows following constraints:

• After collision, the magnitude of velocity either doubles (with probability p) or halves(with probability 1-p).
• For every collision, angle of incidence is equal to angle of reflection irrespective of the change in magnitude of velocity.
• On collsion with corner, the ball will retrace it's path.

You need to calculate the expected time after which the ball first intersects or retraces it's own trajectory.

Input:

Single line containing five space separated integers L V_x V_y P Q

L = Side length of square

V_x = Horizontal component of velocity

Vy = Vertical component of velocity

p (probability of mangitude of velocity being doubled) = P/Q

Output:

Single integer, expected time modulo 10⁹+7

Constraints:

• 1 ≤ L,Q ≤ 10⁹
• 0 ≤ P,V_x,V_y ≤ 10⁹
• 0 ≤ max(V_x,V_y)
• P ≤ Q
• (L*V_x)/V_y is an integer