A uniform horizontal beam of length \( L \) and mass \( M \) is supported by two vertical pillars. Pillar 1 is located at the left end of the beam (\( x = 0 \)), and Pillar 2 is located at a distance \( D \) from the left end, where \( \dfrac{L}{2} < D < L \). A crate of mass \( m \) is placed at the rightmost end of the beam (\( x = L \)). The system remains in static equilibrium.

Which of the following is a correct expression for the magnitude of the upward force \( F_1 \) exerted by Pillar 1 on the beam?