Cart 1 of mass \(m\) travels to the right with initial speed \(v_0\) along a horizontal track with negligible friction toward Cart 2 of mass \(2m\), which is initially at rest. Mounted on Cart 2 is an ideal compressed spring of negligible mass held by a latch. At the instant Cart 1 contacts the latch, the spring is released and expands to its uncompressed length while pushing the carts apart. Which of the following correctly pairs the direction of the net impulse exerted on Cart 1 with the sign of the net work done by the spring on the two-cart system during the interaction?