Block 1 of mass \(m_1\) rests on a frictionless horizontal tabletop and is connected by a light, inextensible string passing over a frictionless, massless pulley to hanging block 2 of mass \(m_2\).

The system is released from rest, and block 2 accelerates downward through a vertical distance \(d\) while block 1 remains on the tabletop.

In terms of the magnitude of the string tension \(T\) and the distance \(d\), which of the following correctly gives the changes in mechanical energy \(\Delta E_1\), \(\Delta E_2\), and \(\Delta E_{\text{sys}}\) for the block 1–Earth system, the block 2–Earth system, and the two-block–Earth system, respectively?