A cart of mass \(m_1\) moves to the right with initial speed \(v_0\) along a frictionless horizontal track toward a second cart of mass \(m_2\), which is initially at rest. Attached to the left bumper of the second cart is an ideal, massless spring with force constant \(k\). During the collision, the carts interact solely through the spring. In terms of the given quantities, what is the maximum compression of the spring during the interaction?