Moving relative to camera direction at constant speed (Velocity problem)

Alright, so I want to move a gameObject (Player) relative to the direction that its camera is facing without affecting height (and gravity).

This is my actual code that returns as a function a Vector3 that indicates the velocity to move the player relative to the forward of the camera.

 private Vector3 GetBaseInput()
     { 
         //Return Vector3 of 0 if no key pressed.
         Vector3 p_Velocity = new Vector3();
         if (Input.GetKey(KeyCode.W))
         {
             p_Velocity += cam.transform.forward;
         }
         if (Input.GetKey(KeyCode.S))
         {
             p_Velocity += -cam.transform.forward;
         }
         if (Input.GetKey(KeyCode.A))
         {
             p_Velocity += -cam.transform.right;
         }
         if (Input.GetKey(KeyCode.D))
         {
             p_Velocity += cam.transform.right;
         }
         p_Velocity.Set(p_Velocity.x, rb.velocity.y, p_Velocity.z);
         Vector3.
         return p_Velocity;
     }

However, although this doesn't affect Y position of the player at all, the velocity given by W and S keys is slow if I walk while watching to the ground or to the sky.

I want to move at a constant speed to the direction that the player is facing, without affecting its Y position. How can I achieve this?

PS: Sorry for my bad english or explanation, I don't speak english natively.