Least Powerful GTX 1080 usable CPU without creating a bottleneck

I'm trying to create the most affordable gtx 1080 rig I can think of. I've got all my parts set out but my only problem is the CPU. I figured that the i7-6700k would be the safest choice but I'm sure there are cheaper options that wouldn't be bottlenecked. Also I would prefer a skylake chip so that I could go with a more affordable 1 series motherboard
 

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