block collision with a spring

1. The problem statement, all variables and given/known data

A 1.0-kg block slides on a frictionless, horizontal air track with an initial velocity of v = 2.0 m/s. It collides with another 1.0-kg block, which is initially at rest. One end of an ideal massless spring of spring constant k = 200 N/m is attached to the second block, so that the moving block does not collide directly with the motionless block, but with the free end of the spring, causing it to compress. As the spring compresses, it causes the first block to slow down, and the second block to start moving.

What is the maximum compression of the spring during the interaction? (Hint: both blocks are never simultaneously at rest, so don’t assume (1/2) kx^2max = (1/2) mv^2 )

2. Relevant equations
[itex] m_a v_a + m_b v_b = m_a v_{af} + m_b v_{bf} [/itex]

[itex] K_1 + U_1 = K_2 + U_2 [/itex]

3. The attempt at a solution

This one has been giving me trouble. I want to split it up into parts. At first I was gonna have the first part be an energy problem where the block compresses the spring but I cant do that because as the problem says the other block will also be moving. Then I wanted to do the first part as the collision using momentum but i cant take their speed after the collision to be the same because the problem says the spring causes the first block to slow down as the second starts moving. I am really confused as to how to set up this problem. Please help point me in the right direction

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