Impossible(?) question

A bunch of bananas hangs from the end of a rope that passes over a light, frictionless pulley. A monkey of mass equal to the mass of bananas hangs from the other end of the rope. The monkey and the bananas are initially balanced and at rest. The rope is infinite, so the monkey can’t just drag the bananas over the pulley. Is it possible for the monkey to somehow get to the bananas?

If the monkey climbs up with the speed v, the bananas will go up at the same speed v. So that’s not an option.
If he climbs down, the same will happen.

If the monkey tries to swing back and forth, he will create a bigger tension in the rope, which will eventually drag the bananas higher and away from him.

Is it a solution to this problem at all?

Thanks in advance.

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